YES Problem 1: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR vNonEmpty x y z) (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(x,y) -> f(y,x) ) ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Problem 1: Problem 1: Commutativity Transform Procedure: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR vNonEmpty x y z) (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Problem 1: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR vNonEmpty x y z) (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Problem 1: Problem 1: Not CS-TRS Procedure: R is not a CS-TRS Problem 1: Linearity Procedure: Linear? YES Problem 1: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR vNonEmpty x y z) (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Huet Levy Procedure: -> Rules: f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) -> Vars: x, y, z, x, y, z, x, y, z, x, y, z -> Rlps: (rule: f(f(x,y),z) -> f(x,f(y,z)), id: 1, possubterms: f(f(x,y),z)->[], f(x,y)->[1]) (rule: f(f(y,x),z) -> f(x,f(y,z)), id: 2, possubterms: f(f(y,x),z)->[], f(y,x)->[1]) (rule: f(z,f(x,y)) -> f(x,f(y,z)), id: 3, possubterms: f(z,f(x,y))->[], f(x,y)->[2]) (rule: f(z,f(y,x)) -> f(x,f(y,z)), id: 4, possubterms: f(z,f(y,x))->[], f(y,x)->[2]) -> Unifications: (R1 unifies with R1 at p: [1], l: f(f(x,y),z), lp: f(x,y), sig: {x -> f(x',y'),y -> z'}, l': f(f(x',y'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R1 unifies with R2 at p: [1], l: f(f(x,y),z), lp: f(x,y), sig: {x -> f(y',x'),y -> z'}, l': f(f(y',x'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R1 unifies with R3 at p: [1], l: f(f(x,y),z), lp: f(x,y), sig: {x -> z',y -> f(x',y')}, l': f(z',f(x',y')), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R1 unifies with R4 at p: [1], l: f(f(x,y),z), lp: f(x,y), sig: {x -> z',y -> f(y',x')}, l': f(z',f(y',x')), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R2 unifies with R1 at p: [], l: f(f(y,x),z), lp: f(f(y,x),z), sig: {x -> y',y -> x',z -> z'}, l': f(f(x',y'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R2 unifies with R1 at p: [1], l: f(f(y,x),z), lp: f(y,x), sig: {x -> z',y -> f(x',y')}, l': f(f(x',y'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R2 unifies with R2 at p: [1], l: f(f(y,x),z), lp: f(y,x), sig: {x -> z',y -> f(y',x')}, l': f(f(y',x'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R2 unifies with R3 at p: [1], l: f(f(y,x),z), lp: f(y,x), sig: {x -> f(x',y'),y -> z'}, l': f(z',f(x',y')), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R2 unifies with R4 at p: [1], l: f(f(y,x),z), lp: f(y,x), sig: {x -> f(y',x'),y -> z'}, l': f(z',f(y',x')), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R3 unifies with R1 at p: [], l: f(z,f(x,y)), lp: f(z,f(x,y)), sig: {z -> f(x',y'),z' -> f(x,y)}, l': f(f(x',y'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R3 unifies with R2 at p: [], l: f(z,f(x,y)), lp: f(z,f(x,y)), sig: {z -> f(y',x'),z' -> f(x,y)}, l': f(f(y',x'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R3 unifies with R1 at p: [2], l: f(z,f(x,y)), lp: f(x,y), sig: {x -> f(x',y'),y -> z'}, l': f(f(x',y'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R3 unifies with R2 at p: [2], l: f(z,f(x,y)), lp: f(x,y), sig: {x -> f(y',x'),y -> z'}, l': f(f(y',x'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R3 unifies with R3 at p: [2], l: f(z,f(x,y)), lp: f(x,y), sig: {x -> z',y -> f(x',y')}, l': f(z',f(x',y')), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R3 unifies with R4 at p: [2], l: f(z,f(x,y)), lp: f(x,y), sig: {x -> z',y -> f(y',x')}, l': f(z',f(y',x')), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R4 unifies with R1 at p: [], l: f(z,f(y,x)), lp: f(z,f(y,x)), sig: {z -> f(x',y'),z' -> f(y,x)}, l': f(f(x',y'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R4 unifies with R2 at p: [], l: f(z,f(y,x)), lp: f(z,f(y,x)), sig: {z -> f(y',x'),z' -> f(y,x)}, l': f(f(y',x'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R4 unifies with R3 at p: [], l: f(z,f(y,x)), lp: f(z,f(y,x)), sig: {x -> y',y -> x',z -> z'}, l': f(z',f(x',y')), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R4 unifies with R1 at p: [2], l: f(z,f(y,x)), lp: f(y,x), sig: {x -> z',y -> f(x',y')}, l': f(f(x',y'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R4 unifies with R2 at p: [2], l: f(z,f(y,x)), lp: f(y,x), sig: {x -> z',y -> f(y',x')}, l': f(f(y',x'),z'), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R4 unifies with R3 at p: [2], l: f(z,f(y,x)), lp: f(y,x), sig: {x -> f(x',y'),y -> z'}, l': f(z',f(x',y')), r: f(x,f(y,z)), r': f(x',f(y',z'))) (R4 unifies with R4 at p: [2], l: f(z,f(y,x)), lp: f(y,x), sig: {x -> f(y',x'),y -> z'}, l': f(z',f(y',x')), r: f(x,f(y,z)), r': f(x',f(y',z'))) -> Critical pairs info: => Not trivial, Not overlay, Proper, NW0, N1 => Not trivial, Not overlay, Proper, NW0, N2 => Not trivial, Overlay, Proper, NW0, N3 => Not trivial, Overlay, Proper, NW0, N4 => Not trivial, Not overlay, Proper, NW0, N5 => Not trivial, Overlay, Proper, NW0, N6 => Not trivial, Not overlay, Proper, NW0, N7 => Not trivial, Not overlay, Proper, NW0, N8 => Not trivial, Not overlay, Proper, NW0, N9 => Not trivial, Overlay, Proper, NW0, N10 => Not trivial, Not overlay, Proper, NW0, N11 => Not trivial, Not overlay, Proper, NW0, N12 => Not trivial, Not overlay, Proper, NW0, N13 => Not trivial, Overlay, Proper, NW0, N14 => Not trivial, Not overlay, Proper, NW0, N15 => Not trivial, Not overlay, Proper, NW0, N16 => Not trivial, Not overlay, Proper, NW0, N17 => Not trivial, Not overlay, Proper, NW0, N18 => Not trivial, Not overlay, Proper, NW0, N19 => Not trivial, Not overlay, Proper, NW0, N20 => Not trivial, Overlay, Proper, NW0, N21 => Not trivial, Not overlay, Proper, NW0, N22 -> Problem conclusions: Left linear, Right linear, Linear Not weakly orthogonal, Not almost orthogonal, Not orthogonal Not Huet-Levy confluent, Not Newman confluent R is a TRS The problem is decomposed in 13 subproblems. Problem 1.1: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Not overlay, Proper, NW0, N2 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(f(x',f(y',z')),z) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,13),(3,14),(3,15),(3,16),(4,0),(4,17),(4,18),(4,19),(5,20),(5,21),(5,22),(5,23),(6,11),(6,24),(6,25),(6,26),(7,11),(7,12),(7,27),(7,28),(8,1),(8,2),(8,29),(8,30),(9,31),(9,32),(9,33),(9,34),(10,35),(10,36),(10,37),(10,38),(11,5),(11,6),(11,7),(11,8),(12,1),(12,2),(12,29),(12,30),(13,9),(13,39),(13,40),(13,41),(14,6),(14,29),(14,42),(14,43),(15,0),(15,19),(15,44),(15,45),(16,3),(16,4),(16,46),(16,47),(17,10),(17,42),(17,48),(17,49),(18,5),(18,30),(18,39),(18,50),(19,15),(19,16),(19,51),(19,52),(20,27),(20,43),(20,53),(20,54),(21,11),(21,25),(21,55),(21,56),(22,5),(22,30),(22,39),(22,50),(23,5),(23,6),(23,57),(23,58),(24,28),(24,50),(24,59),(24,60),(25,21),(25,23),(25,61),(25,62),(26,6),(26,29),(26,42),(26,43),(27,32),(27,34),(27,63),(27,64),(28,36),(28,38),(28,65),(28,66),(29,13),(29,14),(29,67),(29,68),(30,12),(30,17),(30,18),(30,69),(31,35),(31,36),(31,37),(31,38),(32,27),(32,43),(32,70),(32,71),(33,9),(33,10),(33,23),(33,68),(34,9),(34,39),(34,72),(34,73),(35,31),(35,32),(35,33),(35,34),(36,28),(36,50),(36,74),(36,75),(37,9),(37,10),(37,11),(37,12),(38,10),(38,42),(38,76),(38,77),(39,27),(39,43),(39,53),(39,54),(40,21),(40,29),(40,36),(40,43),(41,13),(41,14),(41,67),(41,68),(42,28),(42,50),(42,59),(42,60),(43,9),(43,39),(43,40),(43,41),(44,10),(44,42),(44,76),(44,77),(45,5),(45,38),(45,39),(45,67),(46,5),(46,6),(46,57),(46,58),(47,9),(47,10),(47,23),(47,68),(48,25),(48,30),(48,32),(48,50),(49,12),(49,17),(49,18),(49,69),(50,10),(50,42),(50,48),(50,49),(51,9),(51,39),(51,72),(51,73),(52,6),(52,34),(52,42),(52,69),(53,5),(53,38),(53,39),(53,67),(54,20),(54,21),(54,22),(54,23),(55,28),(55,50),(55,74),(55,75),(56,21),(56,29),(56,36),(56,43),(57,29),(57,30),(57,46),(57,47),(58,23),(58,27),(58,28),(58,68),(59,6),(59,34),(59,42),(59,69),(60,11),(60,24),(60,25),(60,26),(61,27),(61,43),(61,70),(61,71),(62,25),(62,30),(62,32),(62,50),(63,36),(63,38),(63,65),(63,66),(64,23),(64,27),(64,28),(64,68),(65,32),(65,34),(65,63),(65,64),(66,11),(66,12),(66,27),(66,28),(67,12),(67,44),(67,45),(67,69),(68,29),(68,30),(68,46),(68,47),(69,51),(69,52),(69,67),(69,68),(70,21),(70,23),(70,61),(70,62),(71,25),(71,32),(71,38),(71,67),(72,51),(72,52),(72,67),(72,68),(73,21),(73,34),(73,36),(73,69),(74,11),(74,25),(74,55),(74,56),(75,21),(75,34),(75,36),(75,69),(76,12),(76,44),(76,45),(76,69),(77,25),(77,32),(77,38),(77,67)] ID: 0 => ('f(f(x',f(y',z')),z)', D0) ID: 1 => ('f(x',f(f(y',z'),z))', D1, R1, P[], S{x8 -> x', x9 -> f(y',z'), x10 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 2 => ('f(f(y',z'),f(x',z))', D1, R2, P[], S{x11 -> f(y',z'), x12 -> x', x13 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 3 => ('f(f(y',f(z',x')),z)', D1, R3, P[1], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 4 => ('f(f(z',f(y',x')),z)', D1, R4, P[1], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 5 => ('f(x',f(y',f(z',z)))', D2, R1, P[2], S{x8 -> y', x9 -> z', x10 -> z}), NR: 'f(y',f(z',z))' ID: 6 => ('f(x',f(z',f(y',z)))', D2, R2, P[2], S{x11 -> z', x12 -> y', x13 -> z}), NR: 'f(z',f(y',z))' ID: 7 => ('f(f(y',z'),f(z,x'))', D2, R3, P[], S{x14 -> f(y',z'), x15 -> z, x16 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 8 => ('f(z,f(f(y',z'),x'))', D2, R4, P[], S{x17 -> z, x18 -> f(y',z'), x19 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 9 => ('f(y',f(z',f(x',z)))', D2, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 10 => ('f(z',f(y',f(x',z)))', D2, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(x',z)}), NR: 'f(z',f(y',f(x',z)))' ID: 11 => ('f(x',f(z,f(y',z')))', D2, R3, P[], S{x14 -> x', x15 -> z, x16 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 12 => ('f(z,f(x',f(y',z')))', D2, R4, P[], S{x17 -> z, x18 -> x', x19 -> f(y',z')}), NR: 'f(z,f(x',f(y',z')))' ID: 13 => ('f(y',f(f(z',x'),z))', D2, R1, P[], S{x8 -> y', x9 -> f(z',x'), x10 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 14 => ('f(f(z',x'),f(y',z))', D2, R2, P[], S{x11 -> f(z',x'), x12 -> y', x13 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 15 => ('f(f(z',f(x',y')),z)', D2, R3, P[1], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 16 => ('f(f(x',f(z',y')),z)', D2, R4, P[1], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 17 => ('f(z',f(f(y',x'),z))', D2, R1, P[], S{x8 -> z', x9 -> f(y',x'), x10 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R2, P[], S{x11 -> f(y',x'), x12 -> z', x13 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(f(y',f(x',z')),z)', D2, R3, P[1], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 20 => ('f(y',f(f(z',z),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 21 => ('f(x',f(z',f(z,y')))', D3, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 22 => ('f(f(z',z),f(y',x'))', D3, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 23 => ('f(x',f(z,f(z',y')))', D3, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 24 => ('f(z',f(f(y',z),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 25 => ('f(x',f(y',f(z,z')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> z'}), NR: 'f(y',f(z,z'))' ID: 26 => ('f(f(y',z),f(z',x'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 27 => ('f(y',f(z',f(z,x')))', D3, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(z,x')}), NR: 'f(y',f(z',f(z,x')))' ID: 28 => ('f(z',f(y',f(z,x')))', D3, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(z,x')}), NR: 'f(z',f(y',f(z,x')))' ID: 29 => ('f(z,f(y',f(z',x')))', D3, R1, P[2], S{x8 -> y', x9 -> z', x10 -> x'}), NR: 'f(y',f(z',x'))' ID: 30 => ('f(z,f(z',f(y',x')))', D3, R2, P[2], S{x11 -> z', x12 -> y', x13 -> x'}), NR: 'f(z',f(y',x'))' ID: 31 => ('f(z',f(f(x',z),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 32 => ('f(y',f(x',f(z,z')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> z'}), NR: 'f(x',f(z,z'))' ID: 33 => ('f(f(x',z),f(z',y'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 34 => ('f(y',f(z,f(x',z')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> z'}), NR: 'f(z,f(x',z'))' ID: 35 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 36 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 37 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 38 => ('f(z',f(z,f(x',y')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 39 => ('f(y',f(x',f(z',z)))', D3, R2, P[2], S{x11 -> x', x12 -> z', x13 -> z}), NR: 'f(x',f(z',z))' ID: 40 => ('f(f(z',x'),f(z,y'))', D3, R3, P[], S{x14 -> f(z',x'), x15 -> z, x16 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 41 => ('f(z,f(f(z',x'),y'))', D3, R4, P[], S{x17 -> z, x18 -> f(z',x'), x19 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 42 => ('f(z',f(x',f(y',z)))', D3, R1, P[], S{x8 -> z', x9 -> x', x10 -> f(y',z)}), NR: 'f(z',f(x',f(y',z)))' ID: 43 => ('f(y',f(z,f(z',x')))', D3, R3, P[], S{x14 -> y', x15 -> z, x16 -> f(z',x')}), NR: 'f(y',f(z,f(z',x')))' ID: 44 => ('f(z',f(f(x',y'),z))', D3, R1, P[], S{x8 -> z', x9 -> f(x',y'), x10 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 45 => ('f(f(x',y'),f(z',z))', D3, R2, P[], S{x11 -> f(x',y'), x12 -> z', x13 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 46 => ('f(x',f(f(z',y'),z))', D3, R1, P[], S{x8 -> x', x9 -> f(z',y'), x10 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 47 => ('f(f(z',y'),f(x',z))', D3, R2, P[], S{x11 -> f(z',y'), x12 -> x', x13 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 48 => ('f(f(y',x'),f(z,z'))', D3, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 49 => ('f(z,f(f(y',x'),z'))', D3, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 50 => ('f(z',f(z,f(y',x')))', D3, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 51 => ('f(y',f(f(x',z'),z))', D3, R1, P[], S{x8 -> y', x9 -> f(x',z'), x10 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 52 => ('f(f(x',z'),f(y',z))', D3, R2, P[], S{x11 -> f(x',z'), x12 -> y', x13 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 53 => ('f(f(z',z),f(x',y'))', D4, R3, P[], S{x14 -> f(z',z), x15 -> x', x16 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 54 => ('f(x',f(f(z',z),y'))', D4, R4, P[], S{x17 -> x', x18 -> f(z',z), x19 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 55 => ('f(z',f(f(z,y'),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 56 => ('f(f(z,y'),f(z',x'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 57 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 58 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 59 => ('f(f(y',z),f(x',z'))', D4, R3, P[], S{x14 -> f(y',z), x15 -> x', x16 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 60 => ('f(x',f(f(y',z),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(y',z), x19 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 61 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 62 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 63 => ('f(z',f(f(z,x'),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 64 => ('f(f(z,x'),f(z',y'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 65 => ('f(y',f(f(z,x'),z'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 66 => ('f(f(z,x'),f(y',z'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 67 => ('f(z,f(z',f(x',y')))', D4, R3, P[2], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 68 => ('f(z,f(x',f(z',y')))', D4, R4, P[2], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 69 => ('f(z,f(y',f(x',z')))', D4, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 70 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 71 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 72 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 73 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 74 => ('f(x',f(f(z,y'),z'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 75 => ('f(f(z,y'),f(x',z'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 76 => ('f(z,f(f(x',y'),z'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 77 => ('f(f(x',y'),f(z,z'))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' t: f(f(x',y'),f(z',z)) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,13),(3,14),(3,15),(3,16),(4,0),(4,17),(4,18),(4,19),(5,9),(5,10),(5,11),(5,12),(6,20),(6,21),(6,22),(6,23),(7,1),(7,2),(7,24),(7,25),(8,1),(8,26),(8,27),(8,28),(9,5),(9,6),(9,7),(9,8),(10,29),(10,30),(10,31),(10,32),(11,1),(11,2),(11,3),(11,4),(12,2),(12,33),(12,34),(12,35),(13,0),(13,17),(13,18),(13,19),(14,24),(14,36),(14,37),(14,38),(15,3),(15,4),(15,23),(15,32),(16,3),(16,39),(16,40),(16,41),(17,13),(17,14),(17,15),(17,16),(18,25),(18,42),(18,43),(18,44),(19,4),(19,45),(19,46),(19,47),(20,24),(20,37),(20,48),(20,49),(21,1),(21,27),(21,50),(21,51),(22,6),(22,12),(22,40),(22,43),(23,6),(23,8),(23,52),(23,53),(24,14),(24,16),(24,54),(24,55),(25,18),(25,19),(25,56),(25,57),(26,25),(26,43),(26,58),(26,59),(27,21),(27,23),(27,60),(27,61),(28,8),(28,10),(28,37),(28,46),(29,3),(29,40),(29,62),(29,63),(30,2),(30,34),(30,64),(30,65),(31,8),(31,10),(31,37),(31,46),(32,10),(32,12),(32,66),(32,67),(33,4),(33,46),(33,68),(33,69),(34,30),(34,32),(34,70),(34,71),(35,6),(35,12),(35,40),(35,43),(36,21),(36,23),(36,60),(36,61),(37,3),(37,40),(37,62),(37,63),(38,14),(38,19),(38,27),(38,30),(39,30),(39,32),(39,70),(39,71),(40,24),(40,37),(40,48),(40,49),(41,16),(41,18),(41,21),(41,34),(42,1),(42,27),(42,50),(42,51),(43,4),(43,46),(43,68),(43,69),(44,16),(44,18),(44,21),(44,34),(45,2),(45,34),(45,64),(45,65),(46,25),(46,43),(46,58),(46,59),(47,14),(47,19),(47,27),(47,30),(48,6),(48,19),(48,30),(48,40),(49,20),(49,21),(49,22),(49,23),(50,25),(50,42),(50,43),(50,44),(51,10),(51,18),(51,21),(51,37),(52,10),(52,12),(52,66),(52,67),(53,23),(53,24),(53,25),(53,32),(54,18),(54,19),(54,56),(54,57),(55,23),(55,24),(55,25),(55,32),(56,14),(56,16),(56,54),(56,55),(57,1),(57,2),(57,24),(57,25),(58,8),(58,16),(58,34),(58,46),(59,1),(59,26),(59,27),(59,28),(60,24),(60,36),(60,37),(60,38),(61,12),(61,14),(61,27),(61,43),(62,10),(62,18),(62,21),(62,37),(63,29),(63,30),(63,31),(63,32),(64,4),(64,45),(64,46),(64,47),(65,6),(65,19),(65,30),(65,40),(66,6),(66,8),(66,52),(66,53),(67,3),(67,4),(67,23),(67,32),(68,12),(68,14),(68,27),(68,43),(69,2),(69,33),(69,34),(69,35),(70,3),(70,39),(70,40),(70,41),(71,8),(71,16),(71,34),(71,46)] ID: 0 => ('f(f(x',y'),f(z',z))', D0) ID: 1 => ('f(x',f(y',f(z',z)))', D1, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(z',z)}), NR: 'f(x',f(y',f(z',z)))' ID: 2 => ('f(y',f(x',f(z',z)))', D1, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(z',z)}), NR: 'f(y',f(x',f(z',z)))' ID: 3 => ('f(z',f(z,f(x',y')))', D1, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(x',y')}), NR: 'f(z',f(z,f(x',y')))' ID: 4 => ('f(z,f(z',f(x',y')))', D1, R4, P[], S{x17 -> z, x18 -> z', x19 -> f(x',y')}), NR: 'f(z,f(z',f(x',y')))' ID: 5 => ('f(y',f(f(z',z),x'))', D2, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 6 => ('f(x',f(z',f(z,y')))', D2, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 7 => ('f(f(z',z),f(y',x'))', D2, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 8 => ('f(x',f(z,f(z',y')))', D2, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 9 => ('f(x',f(f(z',z),y'))', D2, R3, P[], S{x14 -> x', x15 -> f(z',z), x16 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 10 => ('f(y',f(z',f(z,x')))', D2, R3, P[2], S{x14 -> z', x15 -> z, x16 -> x'}), NR: 'f(z',f(z,x'))' ID: 11 => ('f(f(z',z),f(x',y'))', D2, R4, P[], S{x17 -> f(z',z), x18 -> x', x19 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 12 => ('f(y',f(z,f(z',x')))', D2, R4, P[2], S{x17 -> z, x18 -> z', x19 -> x'}), NR: 'f(z,f(z',x'))' ID: 13 => ('f(z,f(f(x',y'),z'))', D2, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 14 => ('f(z',f(x',f(y',z)))', D2, R3, P[2], S{x14 -> x', x15 -> y', x16 -> z}), NR: 'f(x',f(y',z))' ID: 15 => ('f(f(x',y'),f(z,z'))', D2, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 16 => ('f(z',f(y',f(x',z)))', D2, R4, P[2], S{x17 -> y', x18 -> x', x19 -> z}), NR: 'f(y',f(x',z))' ID: 17 => ('f(z',f(f(x',y'),z))', D2, R3, P[], S{x14 -> z', x15 -> f(x',y'), x16 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 18 => ('f(z,f(x',f(y',z')))', D2, R3, P[2], S{x14 -> x', x15 -> y', x16 -> z'}), NR: 'f(x',f(y',z'))' ID: 19 => ('f(z,f(y',f(x',z')))', D2, R4, P[2], S{x17 -> y', x18 -> x', x19 -> z'}), NR: 'f(y',f(x',z'))' ID: 20 => ('f(z',f(f(z,y'),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 21 => ('f(x',f(z,f(y',z')))', D3, R3, P[2], S{x14 -> z, x15 -> y', x16 -> z'}), NR: 'f(z,f(y',z'))' ID: 22 => ('f(f(z,y'),f(z',x'))', D3, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 23 => ('f(x',f(y',f(z,z')))', D3, R4, P[2], S{x17 -> y', x18 -> z, x19 -> z'}), NR: 'f(y',f(z,z'))' ID: 24 => ('f(z',f(z,f(y',x')))', D3, R1, P[], S{x8 -> z', x9 -> z, x10 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 25 => ('f(z,f(z',f(y',x')))', D3, R2, P[], S{x11 -> z, x12 -> z', x13 -> f(y',x')}), NR: 'f(z,f(z',f(y',x')))' ID: 26 => ('f(z,f(f(z',y'),x'))', D3, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 27 => ('f(x',f(z',f(y',z)))', D3, R3, P[2], S{x14 -> z', x15 -> y', x16 -> z}), NR: 'f(z',f(y',z))' ID: 28 => ('f(f(z',y'),f(z,x'))', D3, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 29 => ('f(z',f(f(z,x'),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 30 => ('f(y',f(z,f(x',z')))', D3, R3, P[2], S{x14 -> z, x15 -> x', x16 -> z'}), NR: 'f(z,f(x',z'))' ID: 31 => ('f(f(z,x'),f(z',y'))', D3, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 32 => ('f(y',f(x',f(z,z')))', D3, R4, P[2], S{x17 -> x', x18 -> z, x19 -> z'}), NR: 'f(x',f(z,z'))' ID: 33 => ('f(z,f(f(z',x'),y'))', D3, R3, P[], S{x14 -> z, x15 -> f(z',x'), x16 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 34 => ('f(y',f(z',f(x',z)))', D3, R3, P[2], S{x14 -> z', x15 -> x', x16 -> z}), NR: 'f(z',f(x',z))' ID: 35 => ('f(f(z',x'),f(z,y'))', D3, R4, P[], S{x17 -> f(z',x'), x18 -> z, x19 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 36 => ('f(x',f(f(y',z),z'))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z), x16 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 37 => ('f(z',f(y',f(z,x')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> x'}), NR: 'f(y',f(z,x'))' ID: 38 => ('f(f(y',z),f(x',z'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> x', x19 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 39 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 40 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 41 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 42 => ('f(x',f(f(y',z'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 43 => ('f(z,f(y',f(z',x')))', D3, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 44 => ('f(f(y',z'),f(x',z))', D3, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 45 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 46 => ('f(z,f(x',f(z',y')))', D3, R3, P[2], S{x14 -> x', x15 -> z', x16 -> y'}), NR: 'f(x',f(z',y'))' ID: 47 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 48 => ('f(f(z,y'),f(x',z'))', D4, R3, P[], S{x14 -> f(z,y'), x15 -> x', x16 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 49 => ('f(x',f(f(z,y'),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(z,y'), x19 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 50 => ('f(z,f(f(y',z'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',z'), x16 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 51 => ('f(f(y',z'),f(z,x'))', D4, R4, P[], S{x17 -> f(y',z'), x18 -> z, x19 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 52 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 53 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 54 => ('f(z,f(f(y',x'),z'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',x'), x16 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 55 => ('f(f(y',x'),f(z,z'))', D4, R4, P[], S{x17 -> f(y',x'), x18 -> z, x19 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 56 => ('f(z',f(f(y',x'),z))', D4, R3, P[], S{x14 -> z', x15 -> f(y',x'), x16 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 57 => ('f(f(y',x'),f(z',z))', D4, R4, P[], S{x17 -> f(y',x'), x18 -> z', x19 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 58 => ('f(f(z',y'),f(x',z))', D4, R3, P[], S{x14 -> f(z',y'), x15 -> x', x16 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 59 => ('f(x',f(f(z',y'),z))', D4, R4, P[], S{x17 -> x', x18 -> f(z',y'), x19 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 60 => ('f(z',f(f(y',z),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 61 => ('f(f(y',z),f(z',x'))', D4, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 62 => ('f(f(z,x'),f(y',z'))', D4, R3, P[], S{x14 -> f(z,x'), x15 -> y', x16 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 63 => ('f(y',f(f(z,x'),z'))', D4, R4, P[], S{x17 -> y', x18 -> f(z,x'), x19 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 64 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 65 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 66 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 67 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 68 => ('f(f(z',x'),f(y',z))', D4, R3, P[], S{x14 -> f(z',x'), x15 -> y', x16 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 69 => ('f(y',f(f(z',x'),z))', D4, R4, P[], S{x17 -> y', x18 -> f(z',x'), x19 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 70 => ('f(z',f(f(x',z),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 71 => ('f(f(x',z),f(z',y'))', D4, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' SNodesPath1: f(f(x',f(y',z')),z) -> f(x',f(f(y',z'),z)) TNodesPath1: f(f(x',y'),f(z',z)) -> f(x',f(y',f(z',z))) -> f(y',f(f(z',z),x')) -> f(x',f(f(z',z),y')) -> f(x',f(z',f(z,y'))) -> f(z',f(f(z,y'),x')) -> f(z',f(z,f(y',x'))) -> f(z',f(x',f(y',z))) -> f(x',f(f(y',z),z')) -> f(x',f(z,f(y',z'))) -> f(x',f(z',f(y',z))) -> f(x',f(y',f(z,z'))) -> f(x',f(z,f(z',y'))) -> f(z,f(f(z',y'),x')) -> f(z,f(z',f(y',x'))) -> f(z,f(x',f(y',z'))) -> f(x',f(f(y',z'),z)) SNodesPath2: TNodesPath2: f(f(x',y'),f(z',z)) f(f(x',f(y',z')),z) ->= f(x',f(f(y',z'),z)) *<- f(f(x',y'),f(z',z)) f(f(x',y'),f(z',z)) ->= f(f(x',y'),f(z',z)) *<- f(f(x',f(y',z')),z) "Strongly closed critical pair" The problem is confluent. Problem 1.2: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Overlay, Proper, NW0, N3 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(x',f(y',f(y,x))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(x',f(y',f(y,x)))', D0) ID: 1 => ('f(y',f(f(y,x),x'))', D1, R3, P[], S{x14 -> y', x15 -> f(y,x), x16 -> x'}), NR: 'f(y',f(f(y,x),x'))' ID: 2 => ('f(x',f(y,f(x,y')))', D1, R3, P[2], S{x14 -> y, x15 -> x, x16 -> y'}), NR: 'f(y,f(x,y'))' ID: 3 => ('f(f(y,x),f(y',x'))', D1, R4, P[], S{x17 -> f(y,x), x18 -> y', x19 -> x'}), NR: 'f(f(y,x),f(y',x'))' ID: 4 => ('f(x',f(x,f(y,y')))', D1, R4, P[2], S{x17 -> x, x18 -> y, x19 -> y'}), NR: 'f(x,f(y,y'))' ID: 5 => ('f(y',f(y,f(x,x')))', D2, R1, P[2], S{x8 -> y, x9 -> x, x10 -> x'}), NR: 'f(y,f(x,x'))' ID: 6 => ('f(y',f(x,f(y,x')))', D2, R2, P[2], S{x11 -> x, x12 -> y, x13 -> x'}), NR: 'f(x,f(y,x'))' ID: 7 => ('f(f(y,x),f(x',y'))', D2, R3, P[], S{x14 -> f(y,x), x15 -> x', x16 -> y'}), NR: 'f(f(y,x),f(x',y'))' ID: 8 => ('f(x',f(f(y,x),y'))', D2, R4, P[], S{x17 -> x', x18 -> f(y,x), x19 -> y'}), NR: 'f(x',f(f(y,x),y'))' ID: 9 => ('f(y,f(f(x,y'),x'))', D2, R3, P[], S{x14 -> y, x15 -> f(x,y'), x16 -> x'}), NR: 'f(y,f(f(x,y'),x'))' ID: 10 => ('f(x',f(x,f(y',y)))', D2, R3, P[2], S{x14 -> x, x15 -> y', x16 -> y}), NR: 'f(x,f(y',y))' ID: 11 => ('f(f(x,y'),f(y,x'))', D2, R4, P[], S{x17 -> f(x,y'), x18 -> y, x19 -> x'}), NR: 'f(f(x,y'),f(y,x'))' ID: 12 => ('f(x',f(y',f(x,y)))', D2, R4, P[2], S{x17 -> y', x18 -> x, x19 -> y}), NR: 'f(y',f(x,y))' ID: 13 => ('f(y,f(x,f(y',x')))', D2, R1, P[], S{x8 -> y, x9 -> x, x10 -> f(y',x')}), NR: 'f(y,f(x,f(y',x')))' ID: 14 => ('f(x,f(y,f(y',x')))', D2, R2, P[], S{x11 -> x, x12 -> y, x13 -> f(y',x')}), NR: 'f(x,f(y,f(y',x')))' ID: 15 => ('f(y',f(x',f(y,x)))', D2, R3, P[], S{x14 -> y', x15 -> x', x16 -> f(y,x)}), NR: 'f(y',f(x',f(y,x)))' ID: 16 => ('f(x,f(f(y,y'),x'))', D2, R3, P[], S{x14 -> x, x15 -> f(y,y'), x16 -> x'}), NR: 'f(x,f(f(y,y'),x'))' ID: 17 => ('f(x',f(y,f(y',x)))', D2, R3, P[2], S{x14 -> y, x15 -> y', x16 -> x}), NR: 'f(y,f(y',x))' ID: 18 => ('f(f(y,y'),f(x,x'))', D2, R4, P[], S{x17 -> f(y,y'), x18 -> x, x19 -> x'}), NR: 'f(f(y,y'),f(x,x'))' ID: 19 => ('f(y,f(f(x,x'),y'))', D3, R3, P[], S{x14 -> y, x15 -> f(x,x'), x16 -> y'}), NR: 'f(y,f(f(x,x'),y'))' ID: 20 => ('f(y',f(x,f(x',y)))', D3, R3, P[2], S{x14 -> x, x15 -> x', x16 -> y}), NR: 'f(x,f(x',y))' ID: 21 => ('f(f(x,x'),f(y,y'))', D3, R4, P[], S{x17 -> f(x,x'), x18 -> y, x19 -> y'}), NR: 'f(f(x,x'),f(y,y'))' ID: 22 => ('f(y',f(x',f(x,y)))', D3, R4, P[2], S{x17 -> x', x18 -> x, x19 -> y}), NR: 'f(x',f(x,y))' ID: 23 => ('f(x,f(f(y,x'),y'))', D3, R3, P[], S{x14 -> x, x15 -> f(y,x'), x16 -> y'}), NR: 'f(x,f(f(y,x'),y'))' ID: 24 => ('f(y',f(y,f(x',x)))', D3, R3, P[2], S{x14 -> y, x15 -> x', x16 -> x}), NR: 'f(y,f(x',x))' ID: 25 => ('f(f(y,x'),f(x,y'))', D3, R4, P[], S{x17 -> f(y,x'), x18 -> x, x19 -> y'}), NR: 'f(f(y,x'),f(x,y'))' ID: 26 => ('f(y,f(x,f(x',y')))', D3, R1, P[], S{x8 -> y, x9 -> x, x10 -> f(x',y')}), NR: 'f(y,f(x,f(x',y')))' ID: 27 => ('f(x,f(y,f(x',y')))', D3, R2, P[], S{x11 -> x, x12 -> y, x13 -> f(x',y')}), NR: 'f(x,f(y,f(x',y')))' ID: 28 => ('f(y,f(y',f(x,x')))', D3, R2, P[2], S{x11 -> y', x12 -> x, x13 -> x'}), NR: 'f(y',f(x,x'))' ID: 29 => ('f(f(x,y'),f(x',y))', D3, R3, P[], S{x14 -> f(x,y'), x15 -> x', x16 -> y}), NR: 'f(f(x,y'),f(x',y))' ID: 30 => ('f(x',f(f(x,y'),y))', D3, R4, P[], S{x17 -> x', x18 -> f(x,y'), x19 -> y}), NR: 'f(x',f(f(x,y'),y))' ID: 31 => ('f(x,f(f(y',y),x'))', D3, R3, P[], S{x14 -> x, x15 -> f(y',y), x16 -> x'}), NR: 'f(x,f(f(y',y),x'))' ID: 32 => ('f(f(y',y),f(x,x'))', D3, R4, P[], S{x17 -> f(y',y), x18 -> x, x19 -> x'}), NR: 'f(f(y',y),f(x,x'))' ID: 33 => ('f(x,f(y',f(y,x')))', D3, R1, P[], S{x8 -> x, x9 -> y', x10 -> f(y,x')}), NR: 'f(x,f(y',f(y,x')))' ID: 34 => ('f(y,f(x',f(x,y')))', D3, R3, P[], S{x14 -> y, x15 -> x', x16 -> f(x,y')}), NR: 'f(y,f(x',f(x,y')))' ID: 35 => ('f(y',f(f(x,y),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(x,y), x16 -> x'}), NR: 'f(y',f(f(x,y),x'))' ID: 36 => ('f(f(x,y),f(y',x'))', D3, R4, P[], S{x17 -> f(x,y), x18 -> y', x19 -> x'}), NR: 'f(f(x,y),f(y',x'))' ID: 37 => ('f(x,f(f(y',x'),y))', D3, R3, P[], S{x14 -> x, x15 -> f(y',x'), x16 -> y}), NR: 'f(x,f(f(y',x'),y))' ID: 38 => ('f(y,f(y',f(x',x)))', D3, R3, P[2], S{x14 -> y', x15 -> x', x16 -> x}), NR: 'f(y',f(x',x))' ID: 39 => ('f(f(y',x'),f(x,y))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> x, x19 -> y}), NR: 'f(f(y',x'),f(x,y))' ID: 40 => ('f(y,f(x',f(y',x)))', D3, R4, P[2], S{x17 -> x', x18 -> y', x19 -> x}), NR: 'f(x',f(y',x))' ID: 41 => ('f(y,f(f(y',x'),x))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x'), x16 -> x}), NR: 'f(y,f(f(y',x'),x))' ID: 42 => ('f(x,f(y',f(x',y)))', D3, R3, P[2], S{x14 -> y', x15 -> x', x16 -> y}), NR: 'f(y',f(x',y))' ID: 43 => ('f(f(y',x'),f(y,x))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> y, x19 -> x}), NR: 'f(f(y',x'),f(y,x))' ID: 44 => ('f(x,f(x',f(y',y)))', D3, R4, P[2], S{x17 -> x', x18 -> y', x19 -> y}), NR: 'f(x',f(y',y))' ID: 45 => ('f(f(y,y'),f(x',x))', D3, R3, P[], S{x14 -> f(y,y'), x15 -> x', x16 -> x}), NR: 'f(f(y,y'),f(x',x))' ID: 46 => ('f(x',f(f(y,y'),x))', D3, R4, P[], S{x17 -> x', x18 -> f(y,y'), x19 -> x}), NR: 'f(x',f(f(y,y'),x))' ID: 47 => ('f(y,f(f(y',x),x'))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x), x16 -> x'}), NR: 'f(y,f(f(y',x),x'))' ID: 48 => ('f(f(y',x),f(y,x'))', D3, R4, P[], S{x17 -> f(y',x), x18 -> y, x19 -> x'}), NR: 'f(f(y',x),f(y,x'))' ID: 49 => ('f(x,f(x',f(y,y')))', D3, R3, P[], S{x14 -> x, x15 -> x', x16 -> f(y,y')}), NR: 'f(x,f(x',f(y,y')))' ID: 50 => ('f(f(x,x'),f(y',y))', D4, R3, P[], S{x14 -> f(x,x'), x15 -> y', x16 -> y}), NR: 'f(f(x,x'),f(y',y))' ID: 51 => ('f(y',f(f(x,x'),y))', D4, R4, P[], S{x17 -> y', x18 -> f(x,x'), x19 -> y}), NR: 'f(y',f(f(x,x'),y))' ID: 52 => ('f(x,f(f(x',y),y'))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y), x16 -> y'}), NR: 'f(x,f(f(x',y),y'))' ID: 53 => ('f(f(x',y),f(x,y'))', D4, R4, P[], S{x17 -> f(x',y), x18 -> x, x19 -> y'}), NR: 'f(f(x',y),f(x,y'))' ID: 54 => ('f(x',f(f(x,y),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y), x16 -> y'}), NR: 'f(x',f(f(x,y),y'))' ID: 55 => ('f(f(x,y),f(x',y'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> x', x19 -> y'}), NR: 'f(f(x,y),f(x',y'))' ID: 56 => ('f(f(y,x'),f(y',x))', D4, R3, P[], S{x14 -> f(y,x'), x15 -> y', x16 -> x}), NR: 'f(f(y,x'),f(y',x))' ID: 57 => ('f(y',f(f(y,x'),x))', D4, R4, P[], S{x17 -> y', x18 -> f(y,x'), x19 -> x}), NR: 'f(y',f(f(y,x'),x))' ID: 58 => ('f(y,f(f(x',x),y'))', D4, R3, P[], S{x14 -> y, x15 -> f(x',x), x16 -> y'}), NR: 'f(y,f(f(x',x),y'))' ID: 59 => ('f(f(x',x),f(y,y'))', D4, R4, P[], S{x17 -> f(x',x), x18 -> y, x19 -> y'}), NR: 'f(f(x',x),f(y,y'))' ID: 60 => ('f(x,f(f(x',y'),y))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y'), x16 -> y}), NR: 'f(x,f(f(x',y'),y))' ID: 61 => ('f(f(x',y'),f(x,y))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> x, x19 -> y}), NR: 'f(f(x',y'),f(x,y))' ID: 62 => ('f(y,f(f(x',y'),x))', D4, R3, P[], S{x14 -> y, x15 -> f(x',y'), x16 -> x}), NR: 'f(y,f(f(x',y'),x))' ID: 63 => ('f(f(x',y'),f(y,x))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> y, x19 -> x}), NR: 'f(f(x',y'),f(y,x))' ID: 64 => ('f(f(y',y),f(x',x))', D4, R3, P[], S{x14 -> f(y',y), x15 -> x', x16 -> x}), NR: 'f(f(y',y),f(x',x))' ID: 65 => ('f(x',f(f(y',y),x))', D4, R4, P[], S{x17 -> x', x18 -> f(y',y), x19 -> x}), NR: 'f(x',f(f(y',y),x))' ID: 66 => ('f(y',f(f(x',x),y))', D4, R3, P[], S{x14 -> y', x15 -> f(x',x), x16 -> y}), NR: 'f(y',f(f(x',x),y))' ID: 67 => ('f(f(x',x),f(y',y))', D4, R4, P[], S{x17 -> f(x',x), x18 -> y', x19 -> y}), NR: 'f(f(x',x),f(y',y))' ID: 68 => ('f(x',f(f(y',x),y))', D4, R3, P[], S{x14 -> x', x15 -> f(y',x), x16 -> y}), NR: 'f(x',f(f(y',x),y))' ID: 69 => ('f(f(y',x),f(x',y))', D4, R4, P[], S{x17 -> f(y',x), x18 -> x', x19 -> y}), NR: 'f(f(y',x),f(x',y))' ID: 70 => ('f(y',f(f(x',y),x))', D4, R3, P[], S{x14 -> y', x15 -> f(x',y), x16 -> x}), NR: 'f(y',f(f(x',y),x))' ID: 71 => ('f(f(x',y),f(y',x))', D4, R4, P[], S{x17 -> f(x',y), x18 -> y', x19 -> x}), NR: 'f(f(x',y),f(y',x))' t: f(x,f(y,f(x',y'))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(x,f(y,f(x',y')))', D0) ID: 1 => ('f(y,f(f(x',y'),x))', D1, R3, P[], S{x14 -> y, x15 -> f(x',y'), x16 -> x}), NR: 'f(y,f(f(x',y'),x))' ID: 2 => ('f(x,f(x',f(y',y)))', D1, R3, P[2], S{x14 -> x', x15 -> y', x16 -> y}), NR: 'f(x',f(y',y))' ID: 3 => ('f(f(x',y'),f(y,x))', D1, R4, P[], S{x17 -> f(x',y'), x18 -> y, x19 -> x}), NR: 'f(f(x',y'),f(y,x))' ID: 4 => ('f(x,f(y',f(x',y)))', D1, R4, P[2], S{x17 -> y', x18 -> x', x19 -> y}), NR: 'f(y',f(x',y))' ID: 5 => ('f(y,f(x',f(y',x)))', D2, R1, P[2], S{x8 -> x', x9 -> y', x10 -> x}), NR: 'f(x',f(y',x))' ID: 6 => ('f(y,f(y',f(x',x)))', D2, R2, P[2], S{x11 -> y', x12 -> x', x13 -> x}), NR: 'f(y',f(x',x))' ID: 7 => ('f(f(x',y'),f(x,y))', D2, R3, P[], S{x14 -> f(x',y'), x15 -> x, x16 -> y}), NR: 'f(f(x',y'),f(x,y))' ID: 8 => ('f(x,f(f(x',y'),y))', D2, R4, P[], S{x17 -> x, x18 -> f(x',y'), x19 -> y}), NR: 'f(x,f(f(x',y'),y))' ID: 9 => ('f(x',f(f(y',y),x))', D2, R3, P[], S{x14 -> x', x15 -> f(y',y), x16 -> x}), NR: 'f(x',f(f(y',y),x))' ID: 10 => ('f(x,f(y',f(y,x')))', D2, R3, P[2], S{x14 -> y', x15 -> y, x16 -> x'}), NR: 'f(y',f(y,x'))' ID: 11 => ('f(f(y',y),f(x',x))', D2, R4, P[], S{x17 -> f(y',y), x18 -> x', x19 -> x}), NR: 'f(f(y',y),f(x',x))' ID: 12 => ('f(x,f(y,f(y',x')))', D2, R4, P[2], S{x17 -> y, x18 -> y', x19 -> x'}), NR: 'f(y,f(y',x'))' ID: 13 => ('f(x',f(y',f(y,x)))', D2, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(y,x)}), NR: 'f(x',f(y',f(y,x)))' ID: 14 => ('f(y',f(x',f(y,x)))', D2, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(y,x)}), NR: 'f(y',f(x',f(y,x)))' ID: 15 => ('f(y,f(x,f(x',y')))', D2, R3, P[], S{x14 -> y, x15 -> x, x16 -> f(x',y')}), NR: 'f(y,f(x,f(x',y')))' ID: 16 => ('f(y',f(f(x',y),x))', D2, R3, P[], S{x14 -> y', x15 -> f(x',y), x16 -> x}), NR: 'f(y',f(f(x',y),x))' ID: 17 => ('f(x,f(x',f(y,y')))', D2, R3, P[2], S{x14 -> x', x15 -> y, x16 -> y'}), NR: 'f(x',f(y,y'))' ID: 18 => ('f(f(x',y),f(y',x))', D2, R4, P[], S{x17 -> f(x',y), x18 -> y', x19 -> x}), NR: 'f(f(x',y),f(y',x))' ID: 19 => ('f(x',f(f(y',x),y))', D3, R3, P[], S{x14 -> x', x15 -> f(y',x), x16 -> y}), NR: 'f(x',f(f(y',x),y))' ID: 20 => ('f(y,f(y',f(x,x')))', D3, R3, P[2], S{x14 -> y', x15 -> x, x16 -> x'}), NR: 'f(y',f(x,x'))' ID: 21 => ('f(f(y',x),f(x',y))', D3, R4, P[], S{x17 -> f(y',x), x18 -> x', x19 -> y}), NR: 'f(f(y',x),f(x',y))' ID: 22 => ('f(y,f(x,f(y',x')))', D3, R4, P[2], S{x17 -> x, x18 -> y', x19 -> x'}), NR: 'f(x,f(y',x'))' ID: 23 => ('f(y',f(f(x',x),y))', D3, R3, P[], S{x14 -> y', x15 -> f(x',x), x16 -> y}), NR: 'f(y',f(f(x',x),y))' ID: 24 => ('f(y,f(x',f(x,y')))', D3, R3, P[2], S{x14 -> x', x15 -> x, x16 -> y'}), NR: 'f(x',f(x,y'))' ID: 25 => ('f(f(x',x),f(y',y))', D3, R4, P[], S{x17 -> f(x',x), x18 -> y', x19 -> y}), NR: 'f(f(x',x),f(y',y))' ID: 26 => ('f(x',f(y',f(x,y)))', D3, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(x,y)}), NR: 'f(x',f(y',f(x,y)))' ID: 27 => ('f(y',f(x',f(x,y)))', D3, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(x,y)}), NR: 'f(y',f(x',f(x,y)))' ID: 28 => ('f(x',f(y,f(y',x)))', D3, R2, P[2], S{x11 -> y, x12 -> y', x13 -> x}), NR: 'f(y,f(y',x))' ID: 29 => ('f(f(y',y),f(x,x'))', D3, R3, P[], S{x14 -> f(y',y), x15 -> x, x16 -> x'}), NR: 'f(f(y',y),f(x,x'))' ID: 30 => ('f(x,f(f(y',y),x'))', D3, R4, P[], S{x17 -> x, x18 -> f(y',y), x19 -> x'}), NR: 'f(x,f(f(y',y),x'))' ID: 31 => ('f(y',f(f(y,x'),x))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x'), x16 -> x}), NR: 'f(y',f(f(y,x'),x))' ID: 32 => ('f(f(y,x'),f(y',x))', D3, R4, P[], S{x17 -> f(y,x'), x18 -> y', x19 -> x}), NR: 'f(f(y,x'),f(y',x))' ID: 33 => ('f(y',f(y,f(x',x)))', D3, R1, P[], S{x8 -> y', x9 -> y, x10 -> f(x',x)}), NR: 'f(y',f(y,f(x',x)))' ID: 34 => ('f(x',f(x,f(y',y)))', D3, R3, P[], S{x14 -> x', x15 -> x, x16 -> f(y',y)}), NR: 'f(x',f(x,f(y',y)))' ID: 35 => ('f(y,f(f(y',x'),x))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x'), x16 -> x}), NR: 'f(y,f(f(y',x'),x))' ID: 36 => ('f(f(y',x'),f(y,x))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> y, x19 -> x}), NR: 'f(f(y',x'),f(y,x))' ID: 37 => ('f(y',f(f(y,x),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x), x16 -> x'}), NR: 'f(y',f(f(y,x),x'))' ID: 38 => ('f(x',f(y,f(x,y')))', D3, R3, P[2], S{x14 -> y, x15 -> x, x16 -> y'}), NR: 'f(y,f(x,y'))' ID: 39 => ('f(f(y,x),f(y',x'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> y', x19 -> x'}), NR: 'f(f(y,x),f(y',x'))' ID: 40 => ('f(x',f(x,f(y,y')))', D3, R4, P[2], S{x17 -> x, x18 -> y, x19 -> y'}), NR: 'f(x,f(y,y'))' ID: 41 => ('f(x',f(f(y,x),y'))', D3, R3, P[], S{x14 -> x', x15 -> f(y,x), x16 -> y'}), NR: 'f(x',f(f(y,x),y'))' ID: 42 => ('f(y',f(y,f(x,x')))', D3, R3, P[2], S{x14 -> y, x15 -> x, x16 -> x'}), NR: 'f(y,f(x,x'))' ID: 43 => ('f(f(y,x),f(x',y'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> x', x19 -> y'}), NR: 'f(f(y,x),f(x',y'))' ID: 44 => ('f(y',f(x,f(y,x')))', D3, R4, P[2], S{x17 -> x, x18 -> y, x19 -> x'}), NR: 'f(x,f(y,x'))' ID: 45 => ('f(f(x',y),f(x,y'))', D3, R3, P[], S{x14 -> f(x',y), x15 -> x, x16 -> y'}), NR: 'f(f(x',y),f(x,y'))' ID: 46 => ('f(x,f(f(x',y),y'))', D3, R4, P[], S{x17 -> x, x18 -> f(x',y), x19 -> y'}), NR: 'f(x,f(f(x',y),y'))' ID: 47 => ('f(x',f(f(y,y'),x))', D3, R3, P[], S{x14 -> x', x15 -> f(y,y'), x16 -> x}), NR: 'f(x',f(f(y,y'),x))' ID: 48 => ('f(f(y,y'),f(x',x))', D3, R4, P[], S{x17 -> f(y,y'), x18 -> x', x19 -> x}), NR: 'f(f(y,y'),f(x',x))' ID: 49 => ('f(y',f(x,f(x',y)))', D3, R3, P[], S{x14 -> y', x15 -> x, x16 -> f(x',y)}), NR: 'f(y',f(x,f(x',y)))' ID: 50 => ('f(f(y',x),f(y,x'))', D4, R3, P[], S{x14 -> f(y',x), x15 -> y, x16 -> x'}), NR: 'f(f(y',x),f(y,x'))' ID: 51 => ('f(y,f(f(y',x),x'))', D4, R4, P[], S{x17 -> y, x18 -> f(y',x), x19 -> x'}), NR: 'f(y,f(f(y',x),x'))' ID: 52 => ('f(y',f(f(x,x'),y))', D4, R3, P[], S{x14 -> y', x15 -> f(x,x'), x16 -> y}), NR: 'f(y',f(f(x,x'),y))' ID: 53 => ('f(f(x,x'),f(y',y))', D4, R4, P[], S{x17 -> f(x,x'), x18 -> y', x19 -> y}), NR: 'f(f(x,x'),f(y',y))' ID: 54 => ('f(x,f(f(y',x'),y))', D4, R3, P[], S{x14 -> x, x15 -> f(y',x'), x16 -> y}), NR: 'f(x,f(f(y',x'),y))' ID: 55 => ('f(f(y',x'),f(x,y))', D4, R4, P[], S{x17 -> f(y',x'), x18 -> x, x19 -> y}), NR: 'f(f(y',x'),f(x,y))' ID: 56 => ('f(f(x',x),f(y,y'))', D4, R3, P[], S{x14 -> f(x',x), x15 -> y, x16 -> y'}), NR: 'f(f(x',x),f(y,y'))' ID: 57 => ('f(y,f(f(x',x),y'))', D4, R4, P[], S{x17 -> y, x18 -> f(x',x), x19 -> y'}), NR: 'f(y,f(f(x',x),y'))' ID: 58 => ('f(x',f(f(x,y'),y))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y'), x16 -> y}), NR: 'f(x',f(f(x,y'),y))' ID: 59 => ('f(f(x,y'),f(x',y))', D4, R4, P[], S{x17 -> f(x,y'), x18 -> x', x19 -> y}), NR: 'f(f(x,y'),f(x',y))' ID: 60 => ('f(y',f(f(x,y),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(x,y), x16 -> x'}), NR: 'f(y',f(f(x,y),x'))' ID: 61 => ('f(f(x,y),f(y',x'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> y', x19 -> x'}), NR: 'f(f(x,y),f(y',x'))' ID: 62 => ('f(x',f(f(x,y),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y), x16 -> y'}), NR: 'f(x',f(f(x,y),y'))' ID: 63 => ('f(f(x,y),f(x',y'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> x', x19 -> y'}), NR: 'f(f(x,y),f(x',y'))' ID: 64 => ('f(f(y,x'),f(x,y'))', D4, R3, P[], S{x14 -> f(y,x'), x15 -> x, x16 -> y'}), NR: 'f(f(y,x'),f(x,y'))' ID: 65 => ('f(x,f(f(y,x'),y'))', D4, R4, P[], S{x17 -> x, x18 -> f(y,x'), x19 -> y'}), NR: 'f(x,f(f(y,x'),y'))' ID: 66 => ('f(y,f(f(x,y'),x'))', D4, R3, P[], S{x14 -> y, x15 -> f(x,y'), x16 -> x'}), NR: 'f(y,f(f(x,y'),x'))' ID: 67 => ('f(f(x,y'),f(y,x'))', D4, R4, P[], S{x17 -> f(x,y'), x18 -> y, x19 -> x'}), NR: 'f(f(x,y'),f(y,x'))' ID: 68 => ('f(x,f(f(y,y'),x'))', D4, R3, P[], S{x14 -> x, x15 -> f(y,y'), x16 -> x'}), NR: 'f(x,f(f(y,y'),x'))' ID: 69 => ('f(f(y,y'),f(x,x'))', D4, R4, P[], S{x17 -> f(y,y'), x18 -> x, x19 -> x'}), NR: 'f(f(y,y'),f(x,x'))' ID: 70 => ('f(y,f(f(x,x'),y'))', D4, R3, P[], S{x14 -> y, x15 -> f(x,x'), x16 -> y'}), NR: 'f(y,f(f(x,x'),y'))' ID: 71 => ('f(f(x,x'),f(y,y'))', D4, R4, P[], S{x17 -> f(x,x'), x18 -> y, x19 -> y'}), NR: 'f(f(x,x'),f(y,y'))' SNodesPath1: f(x',f(y',f(y,x))) TNodesPath1: f(x,f(y,f(x',y'))) -> f(y,f(f(x',y'),x)) -> f(y,f(x',f(y',x))) -> f(x',f(f(y',x),y)) -> f(x',f(y',f(x,y))) -> f(x',f(y,f(x,y'))) -> f(x',f(x,f(y',y))) -> f(x',f(y',f(y,x))) SNodesPath2: f(x',f(y',f(y,x))) -> f(y',f(f(y,x),x')) -> f(y',f(y,f(x,x'))) -> f(y,f(f(x,x'),y')) -> f(y,f(x,f(x',y'))) -> f(y,f(y',f(x',x))) -> f(y,f(x',f(x,y'))) -> f(y,f(x,f(y',x'))) -> f(x,f(f(y',x'),y)) -> f(y,f(f(y',x'),x)) -> f(f(y',x'),f(x,y)) -> f(x',f(y',f(x,y))) -> f(x',f(y,f(x,y'))) -> f(y,f(f(x,y'),x')) -> f(y,f(y',f(x,x'))) -> f(f(x,x'),f(y',y)) -> f(x',f(x,f(y',y))) -> f(x',f(y,f(y',x))) -> f(y,f(f(y',x),x')) -> f(x',f(f(y',x),y)) -> f(f(y',x),f(y,x')) -> f(y',f(x,f(y,x'))) -> f(y',f(x',f(y,x))) -> f(f(y,x),f(x',y')) -> f(x,f(y,f(x',y'))) TNodesPath2: f(x,f(y,f(x',y'))) f(x',f(y',f(y,x))) ->= f(x',f(y',f(y,x))) *<- f(x,f(y,f(x',y'))) f(x,f(y,f(x',y'))) ->= f(x,f(y,f(x',y'))) *<- f(x',f(y',f(y,x))) "Strongly closed critical pair" The problem is confluent. Problem 1.3: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Overlay, Proper, NW0, N6 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(x',f(y',f(y,x))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(x',f(y',f(y,x)))', D0) ID: 1 => ('f(y',f(f(y,x),x'))', D1, R3, P[], S{x14 -> y', x15 -> f(y,x), x16 -> x'}), NR: 'f(y',f(f(y,x),x'))' ID: 2 => ('f(x',f(y,f(x,y')))', D1, R3, P[2], S{x14 -> y, x15 -> x, x16 -> y'}), NR: 'f(y,f(x,y'))' ID: 3 => ('f(f(y,x),f(y',x'))', D1, R4, P[], S{x17 -> f(y,x), x18 -> y', x19 -> x'}), NR: 'f(f(y,x),f(y',x'))' ID: 4 => ('f(x',f(x,f(y,y')))', D1, R4, P[2], S{x17 -> x, x18 -> y, x19 -> y'}), NR: 'f(x,f(y,y'))' ID: 5 => ('f(y',f(y,f(x,x')))', D2, R1, P[2], S{x8 -> y, x9 -> x, x10 -> x'}), NR: 'f(y,f(x,x'))' ID: 6 => ('f(y',f(x,f(y,x')))', D2, R2, P[2], S{x11 -> x, x12 -> y, x13 -> x'}), NR: 'f(x,f(y,x'))' ID: 7 => ('f(f(y,x),f(x',y'))', D2, R3, P[], S{x14 -> f(y,x), x15 -> x', x16 -> y'}), NR: 'f(f(y,x),f(x',y'))' ID: 8 => ('f(x',f(f(y,x),y'))', D2, R4, P[], S{x17 -> x', x18 -> f(y,x), x19 -> y'}), NR: 'f(x',f(f(y,x),y'))' ID: 9 => ('f(y,f(f(x,y'),x'))', D2, R3, P[], S{x14 -> y, x15 -> f(x,y'), x16 -> x'}), NR: 'f(y,f(f(x,y'),x'))' ID: 10 => ('f(x',f(x,f(y',y)))', D2, R3, P[2], S{x14 -> x, x15 -> y', x16 -> y}), NR: 'f(x,f(y',y))' ID: 11 => ('f(f(x,y'),f(y,x'))', D2, R4, P[], S{x17 -> f(x,y'), x18 -> y, x19 -> x'}), NR: 'f(f(x,y'),f(y,x'))' ID: 12 => ('f(x',f(y',f(x,y)))', D2, R4, P[2], S{x17 -> y', x18 -> x, x19 -> y}), NR: 'f(y',f(x,y))' ID: 13 => ('f(y,f(x,f(y',x')))', D2, R1, P[], S{x8 -> y, x9 -> x, x10 -> f(y',x')}), NR: 'f(y,f(x,f(y',x')))' ID: 14 => ('f(x,f(y,f(y',x')))', D2, R2, P[], S{x11 -> x, x12 -> y, x13 -> f(y',x')}), NR: 'f(x,f(y,f(y',x')))' ID: 15 => ('f(y',f(x',f(y,x)))', D2, R3, P[], S{x14 -> y', x15 -> x', x16 -> f(y,x)}), NR: 'f(y',f(x',f(y,x)))' ID: 16 => ('f(x,f(f(y,y'),x'))', D2, R3, P[], S{x14 -> x, x15 -> f(y,y'), x16 -> x'}), NR: 'f(x,f(f(y,y'),x'))' ID: 17 => ('f(x',f(y,f(y',x)))', D2, R3, P[2], S{x14 -> y, x15 -> y', x16 -> x}), NR: 'f(y,f(y',x))' ID: 18 => ('f(f(y,y'),f(x,x'))', D2, R4, P[], S{x17 -> f(y,y'), x18 -> x, x19 -> x'}), NR: 'f(f(y,y'),f(x,x'))' ID: 19 => ('f(y,f(f(x,x'),y'))', D3, R3, P[], S{x14 -> y, x15 -> f(x,x'), x16 -> y'}), NR: 'f(y,f(f(x,x'),y'))' ID: 20 => ('f(y',f(x,f(x',y)))', D3, R3, P[2], S{x14 -> x, x15 -> x', x16 -> y}), NR: 'f(x,f(x',y))' ID: 21 => ('f(f(x,x'),f(y,y'))', D3, R4, P[], S{x17 -> f(x,x'), x18 -> y, x19 -> y'}), NR: 'f(f(x,x'),f(y,y'))' ID: 22 => ('f(y',f(x',f(x,y)))', D3, R4, P[2], S{x17 -> x', x18 -> x, x19 -> y}), NR: 'f(x',f(x,y))' ID: 23 => ('f(x,f(f(y,x'),y'))', D3, R3, P[], S{x14 -> x, x15 -> f(y,x'), x16 -> y'}), NR: 'f(x,f(f(y,x'),y'))' ID: 24 => ('f(y',f(y,f(x',x)))', D3, R3, P[2], S{x14 -> y, x15 -> x', x16 -> x}), NR: 'f(y,f(x',x))' ID: 25 => ('f(f(y,x'),f(x,y'))', D3, R4, P[], S{x17 -> f(y,x'), x18 -> x, x19 -> y'}), NR: 'f(f(y,x'),f(x,y'))' ID: 26 => ('f(y,f(x,f(x',y')))', D3, R1, P[], S{x8 -> y, x9 -> x, x10 -> f(x',y')}), NR: 'f(y,f(x,f(x',y')))' ID: 27 => ('f(x,f(y,f(x',y')))', D3, R2, P[], S{x11 -> x, x12 -> y, x13 -> f(x',y')}), NR: 'f(x,f(y,f(x',y')))' ID: 28 => ('f(y,f(y',f(x,x')))', D3, R2, P[2], S{x11 -> y', x12 -> x, x13 -> x'}), NR: 'f(y',f(x,x'))' ID: 29 => ('f(f(x,y'),f(x',y))', D3, R3, P[], S{x14 -> f(x,y'), x15 -> x', x16 -> y}), NR: 'f(f(x,y'),f(x',y))' ID: 30 => ('f(x',f(f(x,y'),y))', D3, R4, P[], S{x17 -> x', x18 -> f(x,y'), x19 -> y}), NR: 'f(x',f(f(x,y'),y))' ID: 31 => ('f(x,f(f(y',y),x'))', D3, R3, P[], S{x14 -> x, x15 -> f(y',y), x16 -> x'}), NR: 'f(x,f(f(y',y),x'))' ID: 32 => ('f(f(y',y),f(x,x'))', D3, R4, P[], S{x17 -> f(y',y), x18 -> x, x19 -> x'}), NR: 'f(f(y',y),f(x,x'))' ID: 33 => ('f(x,f(y',f(y,x')))', D3, R1, P[], S{x8 -> x, x9 -> y', x10 -> f(y,x')}), NR: 'f(x,f(y',f(y,x')))' ID: 34 => ('f(y,f(x',f(x,y')))', D3, R3, P[], S{x14 -> y, x15 -> x', x16 -> f(x,y')}), NR: 'f(y,f(x',f(x,y')))' ID: 35 => ('f(y',f(f(x,y),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(x,y), x16 -> x'}), NR: 'f(y',f(f(x,y),x'))' ID: 36 => ('f(f(x,y),f(y',x'))', D3, R4, P[], S{x17 -> f(x,y), x18 -> y', x19 -> x'}), NR: 'f(f(x,y),f(y',x'))' ID: 37 => ('f(x,f(f(y',x'),y))', D3, R3, P[], S{x14 -> x, x15 -> f(y',x'), x16 -> y}), NR: 'f(x,f(f(y',x'),y))' ID: 38 => ('f(y,f(y',f(x',x)))', D3, R3, P[2], S{x14 -> y', x15 -> x', x16 -> x}), NR: 'f(y',f(x',x))' ID: 39 => ('f(f(y',x'),f(x,y))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> x, x19 -> y}), NR: 'f(f(y',x'),f(x,y))' ID: 40 => ('f(y,f(x',f(y',x)))', D3, R4, P[2], S{x17 -> x', x18 -> y', x19 -> x}), NR: 'f(x',f(y',x))' ID: 41 => ('f(y,f(f(y',x'),x))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x'), x16 -> x}), NR: 'f(y,f(f(y',x'),x))' ID: 42 => ('f(x,f(y',f(x',y)))', D3, R3, P[2], S{x14 -> y', x15 -> x', x16 -> y}), NR: 'f(y',f(x',y))' ID: 43 => ('f(f(y',x'),f(y,x))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> y, x19 -> x}), NR: 'f(f(y',x'),f(y,x))' ID: 44 => ('f(x,f(x',f(y',y)))', D3, R4, P[2], S{x17 -> x', x18 -> y', x19 -> y}), NR: 'f(x',f(y',y))' ID: 45 => ('f(f(y,y'),f(x',x))', D3, R3, P[], S{x14 -> f(y,y'), x15 -> x', x16 -> x}), NR: 'f(f(y,y'),f(x',x))' ID: 46 => ('f(x',f(f(y,y'),x))', D3, R4, P[], S{x17 -> x', x18 -> f(y,y'), x19 -> x}), NR: 'f(x',f(f(y,y'),x))' ID: 47 => ('f(y,f(f(y',x),x'))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x), x16 -> x'}), NR: 'f(y,f(f(y',x),x'))' ID: 48 => ('f(f(y',x),f(y,x'))', D3, R4, P[], S{x17 -> f(y',x), x18 -> y, x19 -> x'}), NR: 'f(f(y',x),f(y,x'))' ID: 49 => ('f(x,f(x',f(y,y')))', D3, R3, P[], S{x14 -> x, x15 -> x', x16 -> f(y,y')}), NR: 'f(x,f(x',f(y,y')))' ID: 50 => ('f(f(x,x'),f(y',y))', D4, R3, P[], S{x14 -> f(x,x'), x15 -> y', x16 -> y}), NR: 'f(f(x,x'),f(y',y))' ID: 51 => ('f(y',f(f(x,x'),y))', D4, R4, P[], S{x17 -> y', x18 -> f(x,x'), x19 -> y}), NR: 'f(y',f(f(x,x'),y))' ID: 52 => ('f(x,f(f(x',y),y'))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y), x16 -> y'}), NR: 'f(x,f(f(x',y),y'))' ID: 53 => ('f(f(x',y),f(x,y'))', D4, R4, P[], S{x17 -> f(x',y), x18 -> x, x19 -> y'}), NR: 'f(f(x',y),f(x,y'))' ID: 54 => ('f(x',f(f(x,y),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y), x16 -> y'}), NR: 'f(x',f(f(x,y),y'))' ID: 55 => ('f(f(x,y),f(x',y'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> x', x19 -> y'}), NR: 'f(f(x,y),f(x',y'))' ID: 56 => ('f(f(y,x'),f(y',x))', D4, R3, P[], S{x14 -> f(y,x'), x15 -> y', x16 -> x}), NR: 'f(f(y,x'),f(y',x))' ID: 57 => ('f(y',f(f(y,x'),x))', D4, R4, P[], S{x17 -> y', x18 -> f(y,x'), x19 -> x}), NR: 'f(y',f(f(y,x'),x))' ID: 58 => ('f(y,f(f(x',x),y'))', D4, R3, P[], S{x14 -> y, x15 -> f(x',x), x16 -> y'}), NR: 'f(y,f(f(x',x),y'))' ID: 59 => ('f(f(x',x),f(y,y'))', D4, R4, P[], S{x17 -> f(x',x), x18 -> y, x19 -> y'}), NR: 'f(f(x',x),f(y,y'))' ID: 60 => ('f(x,f(f(x',y'),y))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y'), x16 -> y}), NR: 'f(x,f(f(x',y'),y))' ID: 61 => ('f(f(x',y'),f(x,y))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> x, x19 -> y}), NR: 'f(f(x',y'),f(x,y))' ID: 62 => ('f(y,f(f(x',y'),x))', D4, R3, P[], S{x14 -> y, x15 -> f(x',y'), x16 -> x}), NR: 'f(y,f(f(x',y'),x))' ID: 63 => ('f(f(x',y'),f(y,x))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> y, x19 -> x}), NR: 'f(f(x',y'),f(y,x))' ID: 64 => ('f(f(y',y),f(x',x))', D4, R3, P[], S{x14 -> f(y',y), x15 -> x', x16 -> x}), NR: 'f(f(y',y),f(x',x))' ID: 65 => ('f(x',f(f(y',y),x))', D4, R4, P[], S{x17 -> x', x18 -> f(y',y), x19 -> x}), NR: 'f(x',f(f(y',y),x))' ID: 66 => ('f(y',f(f(x',x),y))', D4, R3, P[], S{x14 -> y', x15 -> f(x',x), x16 -> y}), NR: 'f(y',f(f(x',x),y))' ID: 67 => ('f(f(x',x),f(y',y))', D4, R4, P[], S{x17 -> f(x',x), x18 -> y', x19 -> y}), NR: 'f(f(x',x),f(y',y))' ID: 68 => ('f(x',f(f(y',x),y))', D4, R3, P[], S{x14 -> x', x15 -> f(y',x), x16 -> y}), NR: 'f(x',f(f(y',x),y))' ID: 69 => ('f(f(y',x),f(x',y))', D4, R4, P[], S{x17 -> f(y',x), x18 -> x', x19 -> y}), NR: 'f(f(y',x),f(x',y))' ID: 70 => ('f(y',f(f(x',y),x))', D4, R3, P[], S{x14 -> y', x15 -> f(x',y), x16 -> x}), NR: 'f(y',f(f(x',y),x))' ID: 71 => ('f(f(x',y),f(y',x))', D4, R4, P[], S{x17 -> f(x',y), x18 -> y', x19 -> x}), NR: 'f(f(x',y),f(y',x))' t: f(x,f(y,f(y',x'))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(x,f(y,f(y',x')))', D0) ID: 1 => ('f(y,f(f(y',x'),x))', D1, R3, P[], S{x14 -> y, x15 -> f(y',x'), x16 -> x}), NR: 'f(y,f(f(y',x'),x))' ID: 2 => ('f(x,f(y',f(x',y)))', D1, R3, P[2], S{x14 -> y', x15 -> x', x16 -> y}), NR: 'f(y',f(x',y))' ID: 3 => ('f(f(y',x'),f(y,x))', D1, R4, P[], S{x17 -> f(y',x'), x18 -> y, x19 -> x}), NR: 'f(f(y',x'),f(y,x))' ID: 4 => ('f(x,f(x',f(y',y)))', D1, R4, P[2], S{x17 -> x', x18 -> y', x19 -> y}), NR: 'f(x',f(y',y))' ID: 5 => ('f(y,f(y',f(x',x)))', D2, R1, P[2], S{x8 -> y', x9 -> x', x10 -> x}), NR: 'f(y',f(x',x))' ID: 6 => ('f(y,f(x',f(y',x)))', D2, R2, P[2], S{x11 -> x', x12 -> y', x13 -> x}), NR: 'f(x',f(y',x))' ID: 7 => ('f(f(y',x'),f(x,y))', D2, R3, P[], S{x14 -> f(y',x'), x15 -> x, x16 -> y}), NR: 'f(f(y',x'),f(x,y))' ID: 8 => ('f(x,f(f(y',x'),y))', D2, R4, P[], S{x17 -> x, x18 -> f(y',x'), x19 -> y}), NR: 'f(x,f(f(y',x'),y))' ID: 9 => ('f(y',f(f(x',y),x))', D2, R3, P[], S{x14 -> y', x15 -> f(x',y), x16 -> x}), NR: 'f(y',f(f(x',y),x))' ID: 10 => ('f(x,f(x',f(y,y')))', D2, R3, P[2], S{x14 -> x', x15 -> y, x16 -> y'}), NR: 'f(x',f(y,y'))' ID: 11 => ('f(f(x',y),f(y',x))', D2, R4, P[], S{x17 -> f(x',y), x18 -> y', x19 -> x}), NR: 'f(f(x',y),f(y',x))' ID: 12 => ('f(x,f(y,f(x',y')))', D2, R4, P[2], S{x17 -> y, x18 -> x', x19 -> y'}), NR: 'f(y,f(x',y'))' ID: 13 => ('f(y',f(x',f(y,x)))', D2, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(y,x)}), NR: 'f(y',f(x',f(y,x)))' ID: 14 => ('f(x',f(y',f(y,x)))', D2, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(y,x)}), NR: 'f(x',f(y',f(y,x)))' ID: 15 => ('f(y,f(x,f(y',x')))', D2, R3, P[], S{x14 -> y, x15 -> x, x16 -> f(y',x')}), NR: 'f(y,f(x,f(y',x')))' ID: 16 => ('f(x',f(f(y',y),x))', D2, R3, P[], S{x14 -> x', x15 -> f(y',y), x16 -> x}), NR: 'f(x',f(f(y',y),x))' ID: 17 => ('f(x,f(y',f(y,x')))', D2, R3, P[2], S{x14 -> y', x15 -> y, x16 -> x'}), NR: 'f(y',f(y,x'))' ID: 18 => ('f(f(y',y),f(x',x))', D2, R4, P[], S{x17 -> f(y',y), x18 -> x', x19 -> x}), NR: 'f(f(y',y),f(x',x))' ID: 19 => ('f(y',f(f(x',x),y))', D3, R3, P[], S{x14 -> y', x15 -> f(x',x), x16 -> y}), NR: 'f(y',f(f(x',x),y))' ID: 20 => ('f(y,f(x',f(x,y')))', D3, R3, P[2], S{x14 -> x', x15 -> x, x16 -> y'}), NR: 'f(x',f(x,y'))' ID: 21 => ('f(f(x',x),f(y',y))', D3, R4, P[], S{x17 -> f(x',x), x18 -> y', x19 -> y}), NR: 'f(f(x',x),f(y',y))' ID: 22 => ('f(y,f(x,f(x',y')))', D3, R4, P[2], S{x17 -> x, x18 -> x', x19 -> y'}), NR: 'f(x,f(x',y'))' ID: 23 => ('f(x',f(f(y',x),y))', D3, R3, P[], S{x14 -> x', x15 -> f(y',x), x16 -> y}), NR: 'f(x',f(f(y',x),y))' ID: 24 => ('f(y,f(y',f(x,x')))', D3, R3, P[2], S{x14 -> y', x15 -> x, x16 -> x'}), NR: 'f(y',f(x,x'))' ID: 25 => ('f(f(y',x),f(x',y))', D3, R4, P[], S{x17 -> f(y',x), x18 -> x', x19 -> y}), NR: 'f(f(y',x),f(x',y))' ID: 26 => ('f(y',f(x',f(x,y)))', D3, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(x,y)}), NR: 'f(y',f(x',f(x,y)))' ID: 27 => ('f(x',f(y',f(x,y)))', D3, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(x,y)}), NR: 'f(x',f(y',f(x,y)))' ID: 28 => ('f(y',f(y,f(x',x)))', D3, R2, P[2], S{x11 -> y, x12 -> x', x13 -> x}), NR: 'f(y,f(x',x))' ID: 29 => ('f(f(x',y),f(x,y'))', D3, R3, P[], S{x14 -> f(x',y), x15 -> x, x16 -> y'}), NR: 'f(f(x',y),f(x,y'))' ID: 30 => ('f(x,f(f(x',y),y'))', D3, R4, P[], S{x17 -> x, x18 -> f(x',y), x19 -> y'}), NR: 'f(x,f(f(x',y),y'))' ID: 31 => ('f(x',f(f(y,y'),x))', D3, R3, P[], S{x14 -> x', x15 -> f(y,y'), x16 -> x}), NR: 'f(x',f(f(y,y'),x))' ID: 32 => ('f(f(y,y'),f(x',x))', D3, R4, P[], S{x17 -> f(y,y'), x18 -> x', x19 -> x}), NR: 'f(f(y,y'),f(x',x))' ID: 33 => ('f(x',f(y,f(y',x)))', D3, R1, P[], S{x8 -> x', x9 -> y, x10 -> f(y',x)}), NR: 'f(x',f(y,f(y',x)))' ID: 34 => ('f(y',f(x,f(x',y)))', D3, R3, P[], S{x14 -> y', x15 -> x, x16 -> f(x',y)}), NR: 'f(y',f(x,f(x',y)))' ID: 35 => ('f(y,f(f(x',y'),x))', D3, R3, P[], S{x14 -> y, x15 -> f(x',y'), x16 -> x}), NR: 'f(y,f(f(x',y'),x))' ID: 36 => ('f(f(x',y'),f(y,x))', D3, R4, P[], S{x17 -> f(x',y'), x18 -> y, x19 -> x}), NR: 'f(f(x',y'),f(y,x))' ID: 37 => ('f(x',f(f(y,x),y'))', D3, R3, P[], S{x14 -> x', x15 -> f(y,x), x16 -> y'}), NR: 'f(x',f(f(y,x),y'))' ID: 38 => ('f(y',f(y,f(x,x')))', D3, R3, P[2], S{x14 -> y, x15 -> x, x16 -> x'}), NR: 'f(y,f(x,x'))' ID: 39 => ('f(f(y,x),f(x',y'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> x', x19 -> y'}), NR: 'f(f(y,x),f(x',y'))' ID: 40 => ('f(y',f(x,f(y,x')))', D3, R4, P[2], S{x17 -> x, x18 -> y, x19 -> x'}), NR: 'f(x,f(y,x'))' ID: 41 => ('f(y',f(f(y,x),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x), x16 -> x'}), NR: 'f(y',f(f(y,x),x'))' ID: 42 => ('f(x',f(y,f(x,y')))', D3, R3, P[2], S{x14 -> y, x15 -> x, x16 -> y'}), NR: 'f(y,f(x,y'))' ID: 43 => ('f(f(y,x),f(y',x'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> y', x19 -> x'}), NR: 'f(f(y,x),f(y',x'))' ID: 44 => ('f(x',f(x,f(y,y')))', D3, R4, P[2], S{x17 -> x, x18 -> y, x19 -> y'}), NR: 'f(x,f(y,y'))' ID: 45 => ('f(f(y',y),f(x,x'))', D3, R3, P[], S{x14 -> f(y',y), x15 -> x, x16 -> x'}), NR: 'f(f(y',y),f(x,x'))' ID: 46 => ('f(x,f(f(y',y),x'))', D3, R4, P[], S{x17 -> x, x18 -> f(y',y), x19 -> x'}), NR: 'f(x,f(f(y',y),x'))' ID: 47 => ('f(y',f(f(y,x'),x))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x'), x16 -> x}), NR: 'f(y',f(f(y,x'),x))' ID: 48 => ('f(f(y,x'),f(y',x))', D3, R4, P[], S{x17 -> f(y,x'), x18 -> y', x19 -> x}), NR: 'f(f(y,x'),f(y',x))' ID: 49 => ('f(x',f(x,f(y',y)))', D3, R3, P[], S{x14 -> x', x15 -> x, x16 -> f(y',y)}), NR: 'f(x',f(x,f(y',y)))' ID: 50 => ('f(f(x',x),f(y,y'))', D4, R3, P[], S{x14 -> f(x',x), x15 -> y, x16 -> y'}), NR: 'f(f(x',x),f(y,y'))' ID: 51 => ('f(y,f(f(x',x),y'))', D4, R4, P[], S{x17 -> y, x18 -> f(x',x), x19 -> y'}), NR: 'f(y,f(f(x',x),y'))' ID: 52 => ('f(x',f(f(x,y'),y))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y'), x16 -> y}), NR: 'f(x',f(f(x,y'),y))' ID: 53 => ('f(f(x,y'),f(x',y))', D4, R4, P[], S{x17 -> f(x,y'), x18 -> x', x19 -> y}), NR: 'f(f(x,y'),f(x',y))' ID: 54 => ('f(x,f(f(x',y'),y))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y'), x16 -> y}), NR: 'f(x,f(f(x',y'),y))' ID: 55 => ('f(f(x',y'),f(x,y))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> x, x19 -> y}), NR: 'f(f(x',y'),f(x,y))' ID: 56 => ('f(f(y',x),f(y,x'))', D4, R3, P[], S{x14 -> f(y',x), x15 -> y, x16 -> x'}), NR: 'f(f(y',x),f(y,x'))' ID: 57 => ('f(y,f(f(y',x),x'))', D4, R4, P[], S{x17 -> y, x18 -> f(y',x), x19 -> x'}), NR: 'f(y,f(f(y',x),x'))' ID: 58 => ('f(y',f(f(x,x'),y))', D4, R3, P[], S{x14 -> y', x15 -> f(x,x'), x16 -> y}), NR: 'f(y',f(f(x,x'),y))' ID: 59 => ('f(f(x,x'),f(y',y))', D4, R4, P[], S{x17 -> f(x,x'), x18 -> y', x19 -> y}), NR: 'f(f(x,x'),f(y',y))' ID: 60 => ('f(x',f(f(x,y),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y), x16 -> y'}), NR: 'f(x',f(f(x,y),y'))' ID: 61 => ('f(f(x,y),f(x',y'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> x', x19 -> y'}), NR: 'f(f(x,y),f(x',y'))' ID: 62 => ('f(y',f(f(x,y),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(x,y), x16 -> x'}), NR: 'f(y',f(f(x,y),x'))' ID: 63 => ('f(f(x,y),f(y',x'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> y', x19 -> x'}), NR: 'f(f(x,y),f(y',x'))' ID: 64 => ('f(f(y,y'),f(x,x'))', D4, R3, P[], S{x14 -> f(y,y'), x15 -> x, x16 -> x'}), NR: 'f(f(y,y'),f(x,x'))' ID: 65 => ('f(x,f(f(y,y'),x'))', D4, R4, P[], S{x17 -> x, x18 -> f(y,y'), x19 -> x'}), NR: 'f(x,f(f(y,y'),x'))' ID: 66 => ('f(y,f(f(x,x'),y'))', D4, R3, P[], S{x14 -> y, x15 -> f(x,x'), x16 -> y'}), NR: 'f(y,f(f(x,x'),y'))' ID: 67 => ('f(f(x,x'),f(y,y'))', D4, R4, P[], S{x17 -> f(x,x'), x18 -> y, x19 -> y'}), NR: 'f(f(x,x'),f(y,y'))' ID: 68 => ('f(x,f(f(y,x'),y'))', D4, R3, P[], S{x14 -> x, x15 -> f(y,x'), x16 -> y'}), NR: 'f(x,f(f(y,x'),y'))' ID: 69 => ('f(f(y,x'),f(x,y'))', D4, R4, P[], S{x17 -> f(y,x'), x18 -> x, x19 -> y'}), NR: 'f(f(y,x'),f(x,y'))' ID: 70 => ('f(y,f(f(x,y'),x'))', D4, R3, P[], S{x14 -> y, x15 -> f(x,y'), x16 -> x'}), NR: 'f(y,f(f(x,y'),x'))' ID: 71 => ('f(f(x,y'),f(y,x'))', D4, R4, P[], S{x17 -> f(x,y'), x18 -> y, x19 -> x'}), NR: 'f(f(x,y'),f(y,x'))' SNodesPath1: f(x',f(y',f(y,x))) TNodesPath1: f(x,f(y,f(y',x'))) -> f(y,f(f(y',x'),x)) -> f(y,f(y',f(x',x))) -> f(y',f(f(x',x),y)) -> f(y',f(x',f(x,y))) -> f(y',f(y,f(x,x'))) -> f(y',f(x,f(x',y))) -> f(y',f(x',f(y,x))) -> f(x',f(f(y,x),y')) -> f(y',f(f(y,x),x')) -> f(f(y,x),f(x',y')) -> f(x,f(y,f(x',y'))) -> f(x,f(y',f(x',y))) -> f(y',f(f(x',y),x)) -> f(y',f(y,f(x',x))) -> f(f(x',x),f(y,y')) -> f(x,f(x',f(y,y'))) -> f(x,f(y',f(y,x'))) -> f(y',f(f(y,x'),x)) -> f(x,f(f(y,x'),y')) -> f(f(y,x'),f(y',x)) -> f(y,f(x',f(y',x))) -> f(y,f(x,f(y',x'))) -> f(f(y',x'),f(x,y)) -> f(x',f(y',f(x,y))) -> f(x',f(y,f(x,y'))) -> f(x',f(x,f(y',y))) -> f(x',f(y',f(y,x))) SNodesPath2: f(x',f(y',f(y,x))) -> f(y',f(f(y,x),x')) -> f(y',f(y,f(x,x'))) -> f(y,f(f(x,x'),y')) -> f(y,f(x,f(x',y'))) -> f(y,f(y',f(x',x))) -> f(y,f(x',f(x,y'))) -> f(y,f(x,f(y',x'))) -> f(x,f(f(y',x'),y)) -> f(y,f(f(y',x'),x)) -> f(f(y',x'),f(x,y)) -> f(x',f(y',f(x,y))) -> f(x',f(y,f(x,y'))) -> f(y,f(f(x,y'),x')) -> f(y,f(y',f(x,x'))) -> f(f(x,x'),f(y',y)) -> f(x',f(x,f(y',y))) -> f(x',f(y,f(y',x))) -> f(y,f(f(y',x),x')) -> f(x',f(f(y',x),y)) -> f(f(y',x),f(y,x')) -> f(y',f(x,f(y,x'))) -> f(y',f(x',f(y,x))) -> f(f(y,x),f(x',y')) -> f(x,f(y,f(x',y'))) -> f(x,f(y',f(x',y))) -> f(x,f(x',f(y,y'))) -> f(x,f(y,f(y',x'))) TNodesPath2: f(x,f(y,f(y',x'))) f(x',f(y',f(y,x))) ->= f(x',f(y',f(y,x))) *<- f(x,f(y,f(y',x'))) f(x,f(y,f(y',x'))) ->= f(x,f(y,f(y',x'))) *<- f(x',f(y',f(y,x))) "Strongly closed critical pair" The problem is confluent. Problem 1.4: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Not overlay, Proper, NW0, N8 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(z,f(x',f(y',z'))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(z,f(x',f(y',z')))', D0) ID: 1 => ('f(x',f(f(y',z'),z))', D1, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 2 => ('f(z,f(y',f(z',x')))', D1, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 3 => ('f(f(y',z'),f(x',z))', D1, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 4 => ('f(z,f(z',f(y',x')))', D1, R4, P[2], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 5 => ('f(x',f(y',f(z',z)))', D2, R1, P[2], S{x8 -> y', x9 -> z', x10 -> z}), NR: 'f(y',f(z',z))' ID: 6 => ('f(x',f(z',f(y',z)))', D2, R2, P[2], S{x11 -> z', x12 -> y', x13 -> z}), NR: 'f(z',f(y',z))' ID: 7 => ('f(f(y',z'),f(z,x'))', D2, R3, P[], S{x14 -> f(y',z'), x15 -> z, x16 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 8 => ('f(z,f(f(y',z'),x'))', D2, R4, P[], S{x17 -> z, x18 -> f(y',z'), x19 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 9 => ('f(y',f(f(z',x'),z))', D2, R3, P[], S{x14 -> y', x15 -> f(z',x'), x16 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 10 => ('f(z,f(z',f(x',y')))', D2, R3, P[2], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 11 => ('f(f(z',x'),f(y',z))', D2, R4, P[], S{x17 -> f(z',x'), x18 -> y', x19 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 12 => ('f(z,f(x',f(z',y')))', D2, R4, P[2], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 13 => ('f(y',f(z',f(x',z)))', D2, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 14 => ('f(z',f(y',f(x',z)))', D2, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(x',z)}), NR: 'f(z',f(y',f(x',z)))' ID: 15 => ('f(x',f(z,f(y',z')))', D2, R3, P[], S{x14 -> x', x15 -> z, x16 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 16 => ('f(z',f(f(y',x'),z))', D2, R3, P[], S{x14 -> z', x15 -> f(y',x'), x16 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 17 => ('f(z,f(y',f(x',z')))', D2, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R4, P[], S{x17 -> f(y',x'), x18 -> z', x19 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(y',f(f(z',z),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 20 => ('f(x',f(z',f(z,y')))', D3, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 21 => ('f(f(z',z),f(y',x'))', D3, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 22 => ('f(x',f(z,f(z',y')))', D3, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 23 => ('f(z',f(f(y',z),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 24 => ('f(x',f(y',f(z,z')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> z'}), NR: 'f(y',f(z,z'))' ID: 25 => ('f(f(y',z),f(z',x'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 26 => ('f(y',f(z',f(z,x')))', D3, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(z,x')}), NR: 'f(y',f(z',f(z,x')))' ID: 27 => ('f(z',f(y',f(z,x')))', D3, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(z,x')}), NR: 'f(z',f(y',f(z,x')))' ID: 28 => ('f(y',f(x',f(z',z)))', D3, R2, P[2], S{x11 -> x', x12 -> z', x13 -> z}), NR: 'f(x',f(z',z))' ID: 29 => ('f(f(z',x'),f(z,y'))', D3, R3, P[], S{x14 -> f(z',x'), x15 -> z, x16 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 30 => ('f(z,f(f(z',x'),y'))', D3, R4, P[], S{x17 -> z, x18 -> f(z',x'), x19 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 31 => ('f(z',f(f(x',y'),z))', D3, R3, P[], S{x14 -> z', x15 -> f(x',y'), x16 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 32 => ('f(f(x',y'),f(z',z))', D3, R4, P[], S{x17 -> f(x',y'), x18 -> z', x19 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 33 => ('f(z',f(x',f(y',z)))', D3, R1, P[], S{x8 -> z', x9 -> x', x10 -> f(y',z)}), NR: 'f(z',f(x',f(y',z)))' ID: 34 => ('f(y',f(z,f(z',x')))', D3, R3, P[], S{x14 -> y', x15 -> z, x16 -> f(z',x')}), NR: 'f(y',f(z,f(z',x')))' ID: 35 => ('f(x',f(f(z',y'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(z',y'), x16 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 36 => ('f(f(z',y'),f(x',z))', D3, R4, P[], S{x17 -> f(z',y'), x18 -> x', x19 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 37 => ('f(z',f(f(x',z),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 38 => ('f(y',f(x',f(z,z')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> z'}), NR: 'f(x',f(z,z'))' ID: 39 => ('f(f(x',z),f(z',y'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 40 => ('f(y',f(z,f(x',z')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> z'}), NR: 'f(z,f(x',z'))' ID: 41 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 42 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 43 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 44 => ('f(z',f(z,f(x',y')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 45 => ('f(f(y',x'),f(z,z'))', D3, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 46 => ('f(z,f(f(y',x'),z'))', D3, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 47 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 48 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 49 => ('f(z',f(z,f(y',x')))', D3, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 50 => ('f(f(z',z),f(x',y'))', D4, R3, P[], S{x14 -> f(z',z), x15 -> x', x16 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 51 => ('f(x',f(f(z',z),y'))', D4, R4, P[], S{x17 -> x', x18 -> f(z',z), x19 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 52 => ('f(z',f(f(z,y'),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 53 => ('f(f(z,y'),f(z',x'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 54 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 55 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 56 => ('f(f(y',z),f(x',z'))', D4, R3, P[], S{x14 -> f(y',z), x15 -> x', x16 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 57 => ('f(x',f(f(y',z),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(y',z), x19 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 58 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 59 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 60 => ('f(z',f(f(z,x'),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 61 => ('f(f(z,x'),f(z',y'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 62 => ('f(y',f(f(z,x'),z'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 63 => ('f(f(z,x'),f(y',z'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 64 => ('f(f(x',y'),f(z,z'))', D4, R3, P[], S{x14 -> f(x',y'), x15 -> z, x16 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 65 => ('f(z,f(f(x',y'),z'))', D4, R4, P[], S{x17 -> z, x18 -> f(x',y'), x19 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 66 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 67 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 68 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 69 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 70 => ('f(x',f(f(z,y'),z'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 71 => ('f(f(z,y'),f(x',z'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' t: f(z',f(f(x',y'),z)) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,12),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,13),(5,19),(5,20),(5,21),(6,10),(6,12),(6,22),(6,23),(7,1),(7,17),(7,24),(7,25),(8,1),(8,2),(8,26),(8,27),(9,14),(9,24),(9,28),(9,29),(10,6),(10,8),(10,30),(10,31),(11,2),(11,16),(11,19),(11,32),(12,1),(12,2),(12,3),(12,4),(13,33),(13,34),(13,35),(13,36),(14,37),(14,38),(14,39),(14,40),(15,0),(15,16),(15,17),(15,18),(16,41),(16,42),(16,43),(16,44),(17,15),(17,45),(17,46),(17,47),(18,12),(18,15),(18,48),(18,49),(19,25),(19,48),(19,50),(19,51),(20,1),(20,25),(20,38),(20,42),(21,5),(21,6),(21,7),(21,8),(22,14),(22,24),(22,52),(22,53),(23,6),(23,16),(23,19),(23,40),(24,32),(24,49),(24,54),(24,55),(25,13),(25,19),(25,20),(25,21),(26,16),(26,17),(26,56),(26,57),(27,8),(27,13),(27,14),(27,44),(28,2),(28,32),(28,34),(28,46),(29,9),(29,10),(29,11),(29,12),(30,13),(30,19),(30,58),(30,59),(31,10),(31,17),(31,24),(31,36),(32,14),(32,24),(32,28),(32,29),(33,37),(33,38),(33,39),(33,40),(34,25),(34,48),(34,60),(34,61),(35,8),(35,13),(35,14),(35,44),(36,13),(36,19),(36,58),(36,59),(37,33),(37,34),(37,35),(37,36),(38,32),(38,49),(38,62),(38,63),(39,12),(39,13),(39,14),(39,15),(40,14),(40,24),(40,52),(40,53),(41,25),(41,48),(41,50),(41,51),(42,15),(42,46),(42,64),(42,65),(43,2),(43,16),(43,19),(43,32),(44,16),(44,17),(44,56),(44,57),(45,32),(45,49),(45,54),(45,55),(46,42),(46,44),(46,66),(46,67),(47,1),(47,17),(47,24),(47,25),(48,34),(48,36),(48,68),(48,69),(49,38),(49,40),(49,70),(49,71),(50,41),(50,42),(50,43),(50,44),(51,6),(51,16),(51,19),(51,40),(52,6),(52,34),(52,40),(52,46),(53,10),(53,12),(53,22),(53,23),(54,15),(54,45),(54,46),(54,47),(55,10),(55,17),(55,24),(55,36),(56,8),(56,44),(56,48),(56,49),(57,1),(57,2),(57,26),(57,27),(58,10),(58,36),(58,38),(58,42),(59,6),(59,8),(59,30),(59,31),(60,42),(60,44),(60,66),(60,67),(61,6),(61,34),(61,40),(61,46),(62,15),(62,46),(62,64),(62,65),(63,10),(63,36),(63,38),(63,42),(64,32),(64,49),(64,62),(64,63),(65,1),(65,25),(65,38),(65,42),(66,25),(66,48),(66,60),(66,61),(67,2),(67,32),(67,34),(67,46),(68,38),(68,40),(68,70),(68,71),(69,8),(69,44),(69,48),(69,49),(70,34),(70,36),(70,68),(70,69),(71,12),(71,15),(71,48),(71,49)] ID: 0 => ('f(z',f(f(x',y'),z))', D0) ID: 1 => ('f(z',f(x',f(y',z)))', D1, R1, P[2], S{x8 -> x', x9 -> y', x10 -> z}), NR: 'f(x',f(y',z))' ID: 2 => ('f(z',f(y',f(x',z)))', D1, R2, P[2], S{x11 -> y', x12 -> x', x13 -> z}), NR: 'f(y',f(x',z))' ID: 3 => ('f(f(x',y'),f(z,z'))', D1, R3, P[], S{x14 -> f(x',y'), x15 -> z, x16 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 4 => ('f(z,f(f(x',y'),z'))', D1, R4, P[], S{x17 -> z, x18 -> f(x',y'), x19 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 5 => ('f(x',f(f(y',z),z'))', D2, R3, P[], S{x14 -> x', x15 -> f(y',z), x16 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 6 => ('f(z',f(y',f(z,x')))', D2, R3, P[2], S{x14 -> y', x15 -> z, x16 -> x'}), NR: 'f(y',f(z,x'))' ID: 7 => ('f(f(y',z),f(x',z'))', D2, R4, P[], S{x17 -> f(y',z), x18 -> x', x19 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 8 => ('f(z',f(z,f(y',x')))', D2, R4, P[2], S{x17 -> z, x18 -> y', x19 -> x'}), NR: 'f(z,f(y',x'))' ID: 9 => ('f(y',f(f(x',z),z'))', D2, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 10 => ('f(z',f(x',f(z,y')))', D2, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 11 => ('f(f(x',z),f(y',z'))', D2, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 12 => ('f(z',f(z,f(x',y')))', D2, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 13 => ('f(x',f(y',f(z,z')))', D2, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(z,z')}), NR: 'f(x',f(y',f(z,z')))' ID: 14 => ('f(y',f(x',f(z,z')))', D2, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(z,z')}), NR: 'f(y',f(x',f(z,z')))' ID: 15 => ('f(z,f(z',f(x',y')))', D2, R3, P[], S{x14 -> z, x15 -> z', x16 -> f(x',y')}), NR: 'f(z,f(z',f(x',y')))' ID: 16 => ('f(z,f(x',f(y',z')))', D2, R1, P[2], S{x8 -> x', x9 -> y', x10 -> z'}), NR: 'f(x',f(y',z'))' ID: 17 => ('f(z,f(y',f(x',z')))', D2, R2, P[2], S{x11 -> y', x12 -> x', x13 -> z'}), NR: 'f(y',f(x',z'))' ID: 18 => ('f(f(x',y'),f(z',z))', D2, R3, P[], S{x14 -> f(x',y'), x15 -> z', x16 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 19 => ('f(x',f(z,f(y',z')))', D3, R2, P[2], S{x11 -> z, x12 -> y', x13 -> z'}), NR: 'f(z,f(y',z'))' ID: 20 => ('f(f(y',z),f(z',x'))', D3, R3, P[], S{x14 -> f(y',z), x15 -> z', x16 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 21 => ('f(z',f(f(y',z),x'))', D3, R4, P[], S{x17 -> z', x18 -> f(y',z), x19 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 22 => ('f(y',f(f(z,x'),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 23 => ('f(f(z,x'),f(y',z'))', D3, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 24 => ('f(y',f(z,f(x',z')))', D3, R1, P[], S{x8 -> y', x9 -> z, x10 -> f(x',z')}), NR: 'f(y',f(z,f(x',z')))' ID: 25 => ('f(x',f(z',f(y',z)))', D3, R3, P[], S{x14 -> x', x15 -> z', x16 -> f(y',z)}), NR: 'f(x',f(z',f(y',z)))' ID: 26 => ('f(z,f(f(y',x'),z'))', D3, R3, P[], S{x14 -> z, x15 -> f(y',x'), x16 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 27 => ('f(f(y',x'),f(z,z'))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> z, x19 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 28 => ('f(f(x',z),f(z',y'))', D3, R3, P[], S{x14 -> f(x',z), x15 -> z', x16 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 29 => ('f(z',f(f(x',z),y'))', D3, R4, P[], S{x17 -> z', x18 -> f(x',z), x19 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 30 => ('f(x',f(f(z,y'),z'))', D3, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 31 => ('f(f(z,y'),f(x',z'))', D3, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 32 => ('f(y',f(z',f(x',z)))', D3, R3, P[], S{x14 -> y', x15 -> z', x16 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 33 => ('f(y',f(f(z,z'),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 34 => ('f(x',f(z,f(z',y')))', D3, R3, P[2], S{x14 -> z, x15 -> z', x16 -> y'}), NR: 'f(z,f(z',y'))' ID: 35 => ('f(f(z,z'),f(y',x'))', D3, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 36 => ('f(x',f(z',f(z,y')))', D3, R4, P[2], S{x17 -> z', x18 -> z, x19 -> y'}), NR: 'f(z',f(z,y'))' ID: 37 => ('f(x',f(f(z,z'),y'))', D3, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 38 => ('f(y',f(z,f(z',x')))', D3, R3, P[2], S{x14 -> z, x15 -> z', x16 -> x'}), NR: 'f(z,f(z',x'))' ID: 39 => ('f(f(z,z'),f(x',y'))', D3, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 40 => ('f(y',f(z',f(z,x')))', D3, R4, P[2], S{x17 -> z', x18 -> z, x19 -> x'}), NR: 'f(z',f(z,x'))' ID: 41 => ('f(x',f(f(y',z'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 42 => ('f(z,f(y',f(z',x')))', D3, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 43 => ('f(f(y',z'),f(x',z))', D3, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 44 => ('f(z,f(z',f(y',x')))', D3, R4, P[2], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 45 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 46 => ('f(z,f(x',f(z',y')))', D3, R3, P[2], S{x14 -> x', x15 -> z', x16 -> y'}), NR: 'f(x',f(z',y'))' ID: 47 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 48 => ('f(x',f(y',f(z',z)))', D3, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(z',z)}), NR: 'f(x',f(y',f(z',z)))' ID: 49 => ('f(y',f(x',f(z',z)))', D3, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(z',z)}), NR: 'f(y',f(x',f(z',z)))' ID: 50 => ('f(z,f(f(y',z'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',z'), x16 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 51 => ('f(f(y',z'),f(z,x'))', D4, R4, P[], S{x17 -> f(y',z'), x18 -> z, x19 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 52 => ('f(f(z,x'),f(z',y'))', D4, R3, P[], S{x14 -> f(z,x'), x15 -> z', x16 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 53 => ('f(z',f(f(z,x'),y'))', D4, R4, P[], S{x17 -> z', x18 -> f(z,x'), x19 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 54 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 55 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 56 => ('f(f(y',x'),f(z',z))', D4, R3, P[], S{x14 -> f(y',x'), x15 -> z', x16 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 57 => ('f(z',f(f(y',x'),z))', D4, R4, P[], S{x17 -> z', x18 -> f(y',x'), x19 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 58 => ('f(f(z,y'),f(z',x'))', D4, R3, P[], S{x14 -> f(z,y'), x15 -> z', x16 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 59 => ('f(z',f(f(z,y'),x'))', D4, R4, P[], S{x17 -> z', x18 -> f(z,y'), x19 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 60 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 61 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 62 => ('f(z,f(f(z',x'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',x'), x16 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 63 => ('f(f(z',x'),f(z,y'))', D4, R4, P[], S{x17 -> f(z',x'), x18 -> z, x19 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 64 => ('f(y',f(f(z',x'),z))', D4, R3, P[], S{x14 -> y', x15 -> f(z',x'), x16 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 65 => ('f(f(z',x'),f(y',z))', D4, R4, P[], S{x17 -> f(z',x'), x18 -> y', x19 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 66 => ('f(x',f(f(z',y'),z))', D4, R3, P[], S{x14 -> x', x15 -> f(z',y'), x16 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 67 => ('f(f(z',y'),f(x',z))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> x', x19 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 68 => ('f(y',f(f(z',z),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 69 => ('f(f(z',z),f(y',x'))', D4, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 70 => ('f(x',f(f(z',z),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z',z), x16 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 71 => ('f(f(z',z),f(x',y'))', D4, R4, P[], S{x17 -> f(z',z), x18 -> x', x19 -> y'}), NR: 'f(f(z',z),f(x',y'))' SNodesPath1: f(z,f(x',f(y',z'))) TNodesPath1: f(z',f(f(x',y'),z)) -> f(z',f(x',f(y',z))) -> f(x',f(f(y',z),z')) -> f(x',f(y',f(z,z'))) -> f(y',f(f(z,z'),x')) -> f(x',f(f(z,z'),y')) -> f(x',f(z,f(z',y'))) -> f(x',f(z',f(y',z))) -> f(x',f(z,f(y',z'))) -> f(x',f(y',f(z',z))) -> f(x',f(z',f(z,y'))) -> f(f(z,y'),f(z',x')) -> f(z',f(x',f(z,y'))) -> f(z',f(y',f(z,x'))) -> f(z',f(z,f(x',y'))) -> f(z',f(y',f(x',z))) -> f(y',f(f(x',z),z')) -> f(y',f(x',f(z,z'))) -> f(y',f(z,f(z',x'))) -> f(y',f(z',f(x',z))) -> f(y',f(z,f(x',z'))) -> f(y',f(x',f(z',z))) -> f(y',f(z',f(z,x'))) -> f(f(z,x'),f(z',y')) -> f(z,f(x',f(z',y'))) -> f(z,f(y',f(z',x'))) -> f(z,f(z',f(x',y'))) -> f(z,f(x',f(y',z'))) SNodesPath2: TNodesPath2: f(z',f(f(x',y'),z)) f(z,f(x',f(y',z'))) ->= f(z,f(x',f(y',z'))) *<- f(z',f(f(x',y'),z)) f(z',f(f(x',y'),z)) ->= f(z',f(f(x',y'),z)) *<- f(z,f(x',f(y',z'))) "Strongly closed critical pair" The problem is confluent. Problem 1.5: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Overlay, Proper, NW0, N10 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(x',f(y',f(x,y))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(x',f(y',f(x,y)))', D0) ID: 1 => ('f(y',f(f(x,y),x'))', D1, R3, P[], S{x14 -> y', x15 -> f(x,y), x16 -> x'}), NR: 'f(y',f(f(x,y),x'))' ID: 2 => ('f(x',f(x,f(y,y')))', D1, R3, P[2], S{x14 -> x, x15 -> y, x16 -> y'}), NR: 'f(x,f(y,y'))' ID: 3 => ('f(f(x,y),f(y',x'))', D1, R4, P[], S{x17 -> f(x,y), x18 -> y', x19 -> x'}), NR: 'f(f(x,y),f(y',x'))' ID: 4 => ('f(x',f(y,f(x,y')))', D1, R4, P[2], S{x17 -> y, x18 -> x, x19 -> y'}), NR: 'f(y,f(x,y'))' ID: 5 => ('f(y',f(x,f(y,x')))', D2, R1, P[2], S{x8 -> x, x9 -> y, x10 -> x'}), NR: 'f(x,f(y,x'))' ID: 6 => ('f(y',f(y,f(x,x')))', D2, R2, P[2], S{x11 -> y, x12 -> x, x13 -> x'}), NR: 'f(y,f(x,x'))' ID: 7 => ('f(f(x,y),f(x',y'))', D2, R3, P[], S{x14 -> f(x,y), x15 -> x', x16 -> y'}), NR: 'f(f(x,y),f(x',y'))' ID: 8 => ('f(x',f(f(x,y),y'))', D2, R4, P[], S{x17 -> x', x18 -> f(x,y), x19 -> y'}), NR: 'f(x',f(f(x,y),y'))' ID: 9 => ('f(x,f(f(y,y'),x'))', D2, R3, P[], S{x14 -> x, x15 -> f(y,y'), x16 -> x'}), NR: 'f(x,f(f(y,y'),x'))' ID: 10 => ('f(x',f(y,f(y',x)))', D2, R3, P[2], S{x14 -> y, x15 -> y', x16 -> x}), NR: 'f(y,f(y',x))' ID: 11 => ('f(f(y,y'),f(x,x'))', D2, R4, P[], S{x17 -> f(y,y'), x18 -> x, x19 -> x'}), NR: 'f(f(y,y'),f(x,x'))' ID: 12 => ('f(x',f(y',f(y,x)))', D2, R4, P[2], S{x17 -> y', x18 -> y, x19 -> x}), NR: 'f(y',f(y,x))' ID: 13 => ('f(x,f(y,f(y',x')))', D2, R1, P[], S{x8 -> x, x9 -> y, x10 -> f(y',x')}), NR: 'f(x,f(y,f(y',x')))' ID: 14 => ('f(y,f(x,f(y',x')))', D2, R2, P[], S{x11 -> y, x12 -> x, x13 -> f(y',x')}), NR: 'f(y,f(x,f(y',x')))' ID: 15 => ('f(y',f(x',f(x,y)))', D2, R3, P[], S{x14 -> y', x15 -> x', x16 -> f(x,y)}), NR: 'f(y',f(x',f(x,y)))' ID: 16 => ('f(y,f(f(x,y'),x'))', D2, R3, P[], S{x14 -> y, x15 -> f(x,y'), x16 -> x'}), NR: 'f(y,f(f(x,y'),x'))' ID: 17 => ('f(x',f(x,f(y',y)))', D2, R3, P[2], S{x14 -> x, x15 -> y', x16 -> y}), NR: 'f(x,f(y',y))' ID: 18 => ('f(f(x,y'),f(y,x'))', D2, R4, P[], S{x17 -> f(x,y'), x18 -> y, x19 -> x'}), NR: 'f(f(x,y'),f(y,x'))' ID: 19 => ('f(x,f(f(y,x'),y'))', D3, R3, P[], S{x14 -> x, x15 -> f(y,x'), x16 -> y'}), NR: 'f(x,f(f(y,x'),y'))' ID: 20 => ('f(y',f(y,f(x',x)))', D3, R3, P[2], S{x14 -> y, x15 -> x', x16 -> x}), NR: 'f(y,f(x',x))' ID: 21 => ('f(f(y,x'),f(x,y'))', D3, R4, P[], S{x17 -> f(y,x'), x18 -> x, x19 -> y'}), NR: 'f(f(y,x'),f(x,y'))' ID: 22 => ('f(y',f(x',f(y,x)))', D3, R4, P[2], S{x17 -> x', x18 -> y, x19 -> x}), NR: 'f(x',f(y,x))' ID: 23 => ('f(y,f(f(x,x'),y'))', D3, R3, P[], S{x14 -> y, x15 -> f(x,x'), x16 -> y'}), NR: 'f(y,f(f(x,x'),y'))' ID: 24 => ('f(y',f(x,f(x',y)))', D3, R3, P[2], S{x14 -> x, x15 -> x', x16 -> y}), NR: 'f(x,f(x',y))' ID: 25 => ('f(f(x,x'),f(y,y'))', D3, R4, P[], S{x17 -> f(x,x'), x18 -> y, x19 -> y'}), NR: 'f(f(x,x'),f(y,y'))' ID: 26 => ('f(x,f(y,f(x',y')))', D3, R1, P[], S{x8 -> x, x9 -> y, x10 -> f(x',y')}), NR: 'f(x,f(y,f(x',y')))' ID: 27 => ('f(y,f(x,f(x',y')))', D3, R2, P[], S{x11 -> y, x12 -> x, x13 -> f(x',y')}), NR: 'f(y,f(x,f(x',y')))' ID: 28 => ('f(x,f(y',f(y,x')))', D3, R2, P[2], S{x11 -> y', x12 -> y, x13 -> x'}), NR: 'f(y',f(y,x'))' ID: 29 => ('f(f(y,y'),f(x',x))', D3, R3, P[], S{x14 -> f(y,y'), x15 -> x', x16 -> x}), NR: 'f(f(y,y'),f(x',x))' ID: 30 => ('f(x',f(f(y,y'),x))', D3, R4, P[], S{x17 -> x', x18 -> f(y,y'), x19 -> x}), NR: 'f(x',f(f(y,y'),x))' ID: 31 => ('f(y,f(f(y',x),x'))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x), x16 -> x'}), NR: 'f(y,f(f(y',x),x'))' ID: 32 => ('f(f(y',x),f(y,x'))', D3, R4, P[], S{x17 -> f(y',x), x18 -> y, x19 -> x'}), NR: 'f(f(y',x),f(y,x'))' ID: 33 => ('f(y,f(y',f(x,x')))', D3, R1, P[], S{x8 -> y, x9 -> y', x10 -> f(x,x')}), NR: 'f(y,f(y',f(x,x')))' ID: 34 => ('f(x,f(x',f(y,y')))', D3, R3, P[], S{x14 -> x, x15 -> x', x16 -> f(y,y')}), NR: 'f(x,f(x',f(y,y')))' ID: 35 => ('f(y',f(f(y,x),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x), x16 -> x'}), NR: 'f(y',f(f(y,x),x'))' ID: 36 => ('f(f(y,x),f(y',x'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> y', x19 -> x'}), NR: 'f(f(y,x),f(y',x'))' ID: 37 => ('f(y,f(f(y',x'),x))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x'), x16 -> x}), NR: 'f(y,f(f(y',x'),x))' ID: 38 => ('f(x,f(y',f(x',y)))', D3, R3, P[2], S{x14 -> y', x15 -> x', x16 -> y}), NR: 'f(y',f(x',y))' ID: 39 => ('f(f(y',x'),f(y,x))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> y, x19 -> x}), NR: 'f(f(y',x'),f(y,x))' ID: 40 => ('f(x,f(x',f(y',y)))', D3, R4, P[2], S{x17 -> x', x18 -> y', x19 -> y}), NR: 'f(x',f(y',y))' ID: 41 => ('f(x,f(f(y',x'),y))', D3, R3, P[], S{x14 -> x, x15 -> f(y',x'), x16 -> y}), NR: 'f(x,f(f(y',x'),y))' ID: 42 => ('f(y,f(y',f(x',x)))', D3, R3, P[2], S{x14 -> y', x15 -> x', x16 -> x}), NR: 'f(y',f(x',x))' ID: 43 => ('f(f(y',x'),f(x,y))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> x, x19 -> y}), NR: 'f(f(y',x'),f(x,y))' ID: 44 => ('f(y,f(x',f(y',x)))', D3, R4, P[2], S{x17 -> x', x18 -> y', x19 -> x}), NR: 'f(x',f(y',x))' ID: 45 => ('f(f(x,y'),f(x',y))', D3, R3, P[], S{x14 -> f(x,y'), x15 -> x', x16 -> y}), NR: 'f(f(x,y'),f(x',y))' ID: 46 => ('f(x',f(f(x,y'),y))', D3, R4, P[], S{x17 -> x', x18 -> f(x,y'), x19 -> y}), NR: 'f(x',f(f(x,y'),y))' ID: 47 => ('f(x,f(f(y',y),x'))', D3, R3, P[], S{x14 -> x, x15 -> f(y',y), x16 -> x'}), NR: 'f(x,f(f(y',y),x'))' ID: 48 => ('f(f(y',y),f(x,x'))', D3, R4, P[], S{x17 -> f(y',y), x18 -> x, x19 -> x'}), NR: 'f(f(y',y),f(x,x'))' ID: 49 => ('f(y,f(x',f(x,y')))', D3, R3, P[], S{x14 -> y, x15 -> x', x16 -> f(x,y')}), NR: 'f(y,f(x',f(x,y')))' ID: 50 => ('f(f(y,x'),f(y',x))', D4, R3, P[], S{x14 -> f(y,x'), x15 -> y', x16 -> x}), NR: 'f(f(y,x'),f(y',x))' ID: 51 => ('f(y',f(f(y,x'),x))', D4, R4, P[], S{x17 -> y', x18 -> f(y,x'), x19 -> x}), NR: 'f(y',f(f(y,x'),x))' ID: 52 => ('f(y,f(f(x',x),y'))', D4, R3, P[], S{x14 -> y, x15 -> f(x',x), x16 -> y'}), NR: 'f(y,f(f(x',x),y'))' ID: 53 => ('f(f(x',x),f(y,y'))', D4, R4, P[], S{x17 -> f(x',x), x18 -> y, x19 -> y'}), NR: 'f(f(x',x),f(y,y'))' ID: 54 => ('f(x',f(f(y,x),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(y,x), x16 -> y'}), NR: 'f(x',f(f(y,x),y'))' ID: 55 => ('f(f(y,x),f(x',y'))', D4, R4, P[], S{x17 -> f(y,x), x18 -> x', x19 -> y'}), NR: 'f(f(y,x),f(x',y'))' ID: 56 => ('f(f(x,x'),f(y',y))', D4, R3, P[], S{x14 -> f(x,x'), x15 -> y', x16 -> y}), NR: 'f(f(x,x'),f(y',y))' ID: 57 => ('f(y',f(f(x,x'),y))', D4, R4, P[], S{x17 -> y', x18 -> f(x,x'), x19 -> y}), NR: 'f(y',f(f(x,x'),y))' ID: 58 => ('f(x,f(f(x',y),y'))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y), x16 -> y'}), NR: 'f(x,f(f(x',y),y'))' ID: 59 => ('f(f(x',y),f(x,y'))', D4, R4, P[], S{x17 -> f(x',y), x18 -> x, x19 -> y'}), NR: 'f(f(x',y),f(x,y'))' ID: 60 => ('f(y,f(f(x',y'),x))', D4, R3, P[], S{x14 -> y, x15 -> f(x',y'), x16 -> x}), NR: 'f(y,f(f(x',y'),x))' ID: 61 => ('f(f(x',y'),f(y,x))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> y, x19 -> x}), NR: 'f(f(x',y'),f(y,x))' ID: 62 => ('f(x,f(f(x',y'),y))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y'), x16 -> y}), NR: 'f(x,f(f(x',y'),y))' ID: 63 => ('f(f(x',y'),f(x,y))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> x, x19 -> y}), NR: 'f(f(x',y'),f(x,y))' ID: 64 => ('f(f(y',x),f(x',y))', D4, R3, P[], S{x14 -> f(y',x), x15 -> x', x16 -> y}), NR: 'f(f(y',x),f(x',y))' ID: 65 => ('f(x',f(f(y',x),y))', D4, R4, P[], S{x17 -> x', x18 -> f(y',x), x19 -> y}), NR: 'f(x',f(f(y',x),y))' ID: 66 => ('f(y',f(f(x',y),x))', D4, R3, P[], S{x14 -> y', x15 -> f(x',y), x16 -> x}), NR: 'f(y',f(f(x',y),x))' ID: 67 => ('f(f(x',y),f(y',x))', D4, R4, P[], S{x17 -> f(x',y), x18 -> y', x19 -> x}), NR: 'f(f(x',y),f(y',x))' ID: 68 => ('f(x',f(f(y',y),x))', D4, R3, P[], S{x14 -> x', x15 -> f(y',y), x16 -> x}), NR: 'f(x',f(f(y',y),x))' ID: 69 => ('f(f(y',y),f(x',x))', D4, R4, P[], S{x17 -> f(y',y), x18 -> x', x19 -> x}), NR: 'f(f(y',y),f(x',x))' ID: 70 => ('f(y',f(f(x',x),y))', D4, R3, P[], S{x14 -> y', x15 -> f(x',x), x16 -> y}), NR: 'f(y',f(f(x',x),y))' ID: 71 => ('f(f(x',x),f(y',y))', D4, R4, P[], S{x17 -> f(x',x), x18 -> y', x19 -> y}), NR: 'f(f(x',x),f(y',y))' t: f(x,f(y,f(y',x'))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(x,f(y,f(y',x')))', D0) ID: 1 => ('f(y,f(f(y',x'),x))', D1, R3, P[], S{x14 -> y, x15 -> f(y',x'), x16 -> x}), NR: 'f(y,f(f(y',x'),x))' ID: 2 => ('f(x,f(y',f(x',y)))', D1, R3, P[2], S{x14 -> y', x15 -> x', x16 -> y}), NR: 'f(y',f(x',y))' ID: 3 => ('f(f(y',x'),f(y,x))', D1, R4, P[], S{x17 -> f(y',x'), x18 -> y, x19 -> x}), NR: 'f(f(y',x'),f(y,x))' ID: 4 => ('f(x,f(x',f(y',y)))', D1, R4, P[2], S{x17 -> x', x18 -> y', x19 -> y}), NR: 'f(x',f(y',y))' ID: 5 => ('f(y,f(y',f(x',x)))', D2, R1, P[2], S{x8 -> y', x9 -> x', x10 -> x}), NR: 'f(y',f(x',x))' ID: 6 => ('f(y,f(x',f(y',x)))', D2, R2, P[2], S{x11 -> x', x12 -> y', x13 -> x}), NR: 'f(x',f(y',x))' ID: 7 => ('f(f(y',x'),f(x,y))', D2, R3, P[], S{x14 -> f(y',x'), x15 -> x, x16 -> y}), NR: 'f(f(y',x'),f(x,y))' ID: 8 => ('f(x,f(f(y',x'),y))', D2, R4, P[], S{x17 -> x, x18 -> f(y',x'), x19 -> y}), NR: 'f(x,f(f(y',x'),y))' ID: 9 => ('f(y',f(f(x',y),x))', D2, R3, P[], S{x14 -> y', x15 -> f(x',y), x16 -> x}), NR: 'f(y',f(f(x',y),x))' ID: 10 => ('f(x,f(x',f(y,y')))', D2, R3, P[2], S{x14 -> x', x15 -> y, x16 -> y'}), NR: 'f(x',f(y,y'))' ID: 11 => ('f(f(x',y),f(y',x))', D2, R4, P[], S{x17 -> f(x',y), x18 -> y', x19 -> x}), NR: 'f(f(x',y),f(y',x))' ID: 12 => ('f(x,f(y,f(x',y')))', D2, R4, P[2], S{x17 -> y, x18 -> x', x19 -> y'}), NR: 'f(y,f(x',y'))' ID: 13 => ('f(y',f(x',f(y,x)))', D2, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(y,x)}), NR: 'f(y',f(x',f(y,x)))' ID: 14 => ('f(x',f(y',f(y,x)))', D2, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(y,x)}), NR: 'f(x',f(y',f(y,x)))' ID: 15 => ('f(y,f(x,f(y',x')))', D2, R3, P[], S{x14 -> y, x15 -> x, x16 -> f(y',x')}), NR: 'f(y,f(x,f(y',x')))' ID: 16 => ('f(x',f(f(y',y),x))', D2, R3, P[], S{x14 -> x', x15 -> f(y',y), x16 -> x}), NR: 'f(x',f(f(y',y),x))' ID: 17 => ('f(x,f(y',f(y,x')))', D2, R3, P[2], S{x14 -> y', x15 -> y, x16 -> x'}), NR: 'f(y',f(y,x'))' ID: 18 => ('f(f(y',y),f(x',x))', D2, R4, P[], S{x17 -> f(y',y), x18 -> x', x19 -> x}), NR: 'f(f(y',y),f(x',x))' ID: 19 => ('f(y',f(f(x',x),y))', D3, R3, P[], S{x14 -> y', x15 -> f(x',x), x16 -> y}), NR: 'f(y',f(f(x',x),y))' ID: 20 => ('f(y,f(x',f(x,y')))', D3, R3, P[2], S{x14 -> x', x15 -> x, x16 -> y'}), NR: 'f(x',f(x,y'))' ID: 21 => ('f(f(x',x),f(y',y))', D3, R4, P[], S{x17 -> f(x',x), x18 -> y', x19 -> y}), NR: 'f(f(x',x),f(y',y))' ID: 22 => ('f(y,f(x,f(x',y')))', D3, R4, P[2], S{x17 -> x, x18 -> x', x19 -> y'}), NR: 'f(x,f(x',y'))' ID: 23 => ('f(x',f(f(y',x),y))', D3, R3, P[], S{x14 -> x', x15 -> f(y',x), x16 -> y}), NR: 'f(x',f(f(y',x),y))' ID: 24 => ('f(y,f(y',f(x,x')))', D3, R3, P[2], S{x14 -> y', x15 -> x, x16 -> x'}), NR: 'f(y',f(x,x'))' ID: 25 => ('f(f(y',x),f(x',y))', D3, R4, P[], S{x17 -> f(y',x), x18 -> x', x19 -> y}), NR: 'f(f(y',x),f(x',y))' ID: 26 => ('f(y',f(x',f(x,y)))', D3, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(x,y)}), NR: 'f(y',f(x',f(x,y)))' ID: 27 => ('f(x',f(y',f(x,y)))', D3, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(x,y)}), NR: 'f(x',f(y',f(x,y)))' ID: 28 => ('f(y',f(y,f(x',x)))', D3, R2, P[2], S{x11 -> y, x12 -> x', x13 -> x}), NR: 'f(y,f(x',x))' ID: 29 => ('f(f(x',y),f(x,y'))', D3, R3, P[], S{x14 -> f(x',y), x15 -> x, x16 -> y'}), NR: 'f(f(x',y),f(x,y'))' ID: 30 => ('f(x,f(f(x',y),y'))', D3, R4, P[], S{x17 -> x, x18 -> f(x',y), x19 -> y'}), NR: 'f(x,f(f(x',y),y'))' ID: 31 => ('f(x',f(f(y,y'),x))', D3, R3, P[], S{x14 -> x', x15 -> f(y,y'), x16 -> x}), NR: 'f(x',f(f(y,y'),x))' ID: 32 => ('f(f(y,y'),f(x',x))', D3, R4, P[], S{x17 -> f(y,y'), x18 -> x', x19 -> x}), NR: 'f(f(y,y'),f(x',x))' ID: 33 => ('f(x',f(y,f(y',x)))', D3, R1, P[], S{x8 -> x', x9 -> y, x10 -> f(y',x)}), NR: 'f(x',f(y,f(y',x)))' ID: 34 => ('f(y',f(x,f(x',y)))', D3, R3, P[], S{x14 -> y', x15 -> x, x16 -> f(x',y)}), NR: 'f(y',f(x,f(x',y)))' ID: 35 => ('f(y,f(f(x',y'),x))', D3, R3, P[], S{x14 -> y, x15 -> f(x',y'), x16 -> x}), NR: 'f(y,f(f(x',y'),x))' ID: 36 => ('f(f(x',y'),f(y,x))', D3, R4, P[], S{x17 -> f(x',y'), x18 -> y, x19 -> x}), NR: 'f(f(x',y'),f(y,x))' ID: 37 => ('f(x',f(f(y,x),y'))', D3, R3, P[], S{x14 -> x', x15 -> f(y,x), x16 -> y'}), NR: 'f(x',f(f(y,x),y'))' ID: 38 => ('f(y',f(y,f(x,x')))', D3, R3, P[2], S{x14 -> y, x15 -> x, x16 -> x'}), NR: 'f(y,f(x,x'))' ID: 39 => ('f(f(y,x),f(x',y'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> x', x19 -> y'}), NR: 'f(f(y,x),f(x',y'))' ID: 40 => ('f(y',f(x,f(y,x')))', D3, R4, P[2], S{x17 -> x, x18 -> y, x19 -> x'}), NR: 'f(x,f(y,x'))' ID: 41 => ('f(y',f(f(y,x),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x), x16 -> x'}), NR: 'f(y',f(f(y,x),x'))' ID: 42 => ('f(x',f(y,f(x,y')))', D3, R3, P[2], S{x14 -> y, x15 -> x, x16 -> y'}), NR: 'f(y,f(x,y'))' ID: 43 => ('f(f(y,x),f(y',x'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> y', x19 -> x'}), NR: 'f(f(y,x),f(y',x'))' ID: 44 => ('f(x',f(x,f(y,y')))', D3, R4, P[2], S{x17 -> x, x18 -> y, x19 -> y'}), NR: 'f(x,f(y,y'))' ID: 45 => ('f(f(y',y),f(x,x'))', D3, R3, P[], S{x14 -> f(y',y), x15 -> x, x16 -> x'}), NR: 'f(f(y',y),f(x,x'))' ID: 46 => ('f(x,f(f(y',y),x'))', D3, R4, P[], S{x17 -> x, x18 -> f(y',y), x19 -> x'}), NR: 'f(x,f(f(y',y),x'))' ID: 47 => ('f(y',f(f(y,x'),x))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x'), x16 -> x}), NR: 'f(y',f(f(y,x'),x))' ID: 48 => ('f(f(y,x'),f(y',x))', D3, R4, P[], S{x17 -> f(y,x'), x18 -> y', x19 -> x}), NR: 'f(f(y,x'),f(y',x))' ID: 49 => ('f(x',f(x,f(y',y)))', D3, R3, P[], S{x14 -> x', x15 -> x, x16 -> f(y',y)}), NR: 'f(x',f(x,f(y',y)))' ID: 50 => ('f(f(x',x),f(y,y'))', D4, R3, P[], S{x14 -> f(x',x), x15 -> y, x16 -> y'}), NR: 'f(f(x',x),f(y,y'))' ID: 51 => ('f(y,f(f(x',x),y'))', D4, R4, P[], S{x17 -> y, x18 -> f(x',x), x19 -> y'}), NR: 'f(y,f(f(x',x),y'))' ID: 52 => ('f(x',f(f(x,y'),y))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y'), x16 -> y}), NR: 'f(x',f(f(x,y'),y))' ID: 53 => ('f(f(x,y'),f(x',y))', D4, R4, P[], S{x17 -> f(x,y'), x18 -> x', x19 -> y}), NR: 'f(f(x,y'),f(x',y))' ID: 54 => ('f(x,f(f(x',y'),y))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y'), x16 -> y}), NR: 'f(x,f(f(x',y'),y))' ID: 55 => ('f(f(x',y'),f(x,y))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> x, x19 -> y}), NR: 'f(f(x',y'),f(x,y))' ID: 56 => ('f(f(y',x),f(y,x'))', D4, R3, P[], S{x14 -> f(y',x), x15 -> y, x16 -> x'}), NR: 'f(f(y',x),f(y,x'))' ID: 57 => ('f(y,f(f(y',x),x'))', D4, R4, P[], S{x17 -> y, x18 -> f(y',x), x19 -> x'}), NR: 'f(y,f(f(y',x),x'))' ID: 58 => ('f(y',f(f(x,x'),y))', D4, R3, P[], S{x14 -> y', x15 -> f(x,x'), x16 -> y}), NR: 'f(y',f(f(x,x'),y))' ID: 59 => ('f(f(x,x'),f(y',y))', D4, R4, P[], S{x17 -> f(x,x'), x18 -> y', x19 -> y}), NR: 'f(f(x,x'),f(y',y))' ID: 60 => ('f(x',f(f(x,y),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y), x16 -> y'}), NR: 'f(x',f(f(x,y),y'))' ID: 61 => ('f(f(x,y),f(x',y'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> x', x19 -> y'}), NR: 'f(f(x,y),f(x',y'))' ID: 62 => ('f(y',f(f(x,y),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(x,y), x16 -> x'}), NR: 'f(y',f(f(x,y),x'))' ID: 63 => ('f(f(x,y),f(y',x'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> y', x19 -> x'}), NR: 'f(f(x,y),f(y',x'))' ID: 64 => ('f(f(y,y'),f(x,x'))', D4, R3, P[], S{x14 -> f(y,y'), x15 -> x, x16 -> x'}), NR: 'f(f(y,y'),f(x,x'))' ID: 65 => ('f(x,f(f(y,y'),x'))', D4, R4, P[], S{x17 -> x, x18 -> f(y,y'), x19 -> x'}), NR: 'f(x,f(f(y,y'),x'))' ID: 66 => ('f(y,f(f(x,x'),y'))', D4, R3, P[], S{x14 -> y, x15 -> f(x,x'), x16 -> y'}), NR: 'f(y,f(f(x,x'),y'))' ID: 67 => ('f(f(x,x'),f(y,y'))', D4, R4, P[], S{x17 -> f(x,x'), x18 -> y, x19 -> y'}), NR: 'f(f(x,x'),f(y,y'))' ID: 68 => ('f(x,f(f(y,x'),y'))', D4, R3, P[], S{x14 -> x, x15 -> f(y,x'), x16 -> y'}), NR: 'f(x,f(f(y,x'),y'))' ID: 69 => ('f(f(y,x'),f(x,y'))', D4, R4, P[], S{x17 -> f(y,x'), x18 -> x, x19 -> y'}), NR: 'f(f(y,x'),f(x,y'))' ID: 70 => ('f(y,f(f(x,y'),x'))', D4, R3, P[], S{x14 -> y, x15 -> f(x,y'), x16 -> x'}), NR: 'f(y,f(f(x,y'),x'))' ID: 71 => ('f(f(x,y'),f(y,x'))', D4, R4, P[], S{x17 -> f(x,y'), x18 -> y, x19 -> x'}), NR: 'f(f(x,y'),f(y,x'))' SNodesPath1: f(x',f(y',f(x,y))) TNodesPath1: f(x,f(y,f(y',x'))) -> f(y,f(f(y',x'),x)) -> f(y,f(y',f(x',x))) -> f(y',f(f(x',x),y)) -> f(y',f(x',f(x,y))) -> f(y',f(y,f(x,x'))) -> f(y',f(x,f(x',y))) -> f(y',f(x',f(y,x))) -> f(x',f(f(y,x),y')) -> f(y',f(f(y,x),x')) -> f(f(y,x),f(x',y')) -> f(x,f(y,f(x',y'))) -> f(x,f(y',f(x',y))) -> f(y',f(f(x',y),x)) -> f(y',f(y,f(x',x))) -> f(f(x',x),f(y,y')) -> f(x,f(x',f(y,y'))) -> f(x,f(y',f(y,x'))) -> f(y',f(f(y,x'),x)) -> f(x,f(f(y,x'),y')) -> f(f(y,x'),f(y',x)) -> f(y,f(x',f(y',x))) -> f(y,f(x,f(y',x'))) -> f(f(y',x'),f(x,y)) -> f(x',f(y',f(x,y))) SNodesPath2: f(x',f(y',f(x,y))) -> f(y',f(f(x,y),x')) -> f(y',f(x,f(y,x'))) -> f(x,f(f(y,x'),y')) -> f(x,f(y,f(x',y'))) -> f(x,f(y',f(x',y))) -> f(x,f(x',f(y,y'))) -> f(x,f(y,f(y',x'))) TNodesPath2: f(x,f(y,f(y',x'))) f(x',f(y',f(x,y))) ->= f(x',f(y',f(x,y))) *<- f(x,f(y,f(y',x'))) f(x,f(y,f(y',x'))) ->= f(x,f(y,f(y',x'))) *<- f(x',f(y',f(x,y))) "Strongly closed critical pair" The problem is confluent. Problem 1.6: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Overlay, Proper, NW0, N14 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(x',f(y',f(x,y))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(x',f(y',f(x,y)))', D0) ID: 1 => ('f(y',f(f(x,y),x'))', D1, R3, P[], S{x14 -> y', x15 -> f(x,y), x16 -> x'}), NR: 'f(y',f(f(x,y),x'))' ID: 2 => ('f(x',f(x,f(y,y')))', D1, R3, P[2], S{x14 -> x, x15 -> y, x16 -> y'}), NR: 'f(x,f(y,y'))' ID: 3 => ('f(f(x,y),f(y',x'))', D1, R4, P[], S{x17 -> f(x,y), x18 -> y', x19 -> x'}), NR: 'f(f(x,y),f(y',x'))' ID: 4 => ('f(x',f(y,f(x,y')))', D1, R4, P[2], S{x17 -> y, x18 -> x, x19 -> y'}), NR: 'f(y,f(x,y'))' ID: 5 => ('f(y',f(x,f(y,x')))', D2, R1, P[2], S{x8 -> x, x9 -> y, x10 -> x'}), NR: 'f(x,f(y,x'))' ID: 6 => ('f(y',f(y,f(x,x')))', D2, R2, P[2], S{x11 -> y, x12 -> x, x13 -> x'}), NR: 'f(y,f(x,x'))' ID: 7 => ('f(f(x,y),f(x',y'))', D2, R3, P[], S{x14 -> f(x,y), x15 -> x', x16 -> y'}), NR: 'f(f(x,y),f(x',y'))' ID: 8 => ('f(x',f(f(x,y),y'))', D2, R4, P[], S{x17 -> x', x18 -> f(x,y), x19 -> y'}), NR: 'f(x',f(f(x,y),y'))' ID: 9 => ('f(x,f(f(y,y'),x'))', D2, R3, P[], S{x14 -> x, x15 -> f(y,y'), x16 -> x'}), NR: 'f(x,f(f(y,y'),x'))' ID: 10 => ('f(x',f(y,f(y',x)))', D2, R3, P[2], S{x14 -> y, x15 -> y', x16 -> x}), NR: 'f(y,f(y',x))' ID: 11 => ('f(f(y,y'),f(x,x'))', D2, R4, P[], S{x17 -> f(y,y'), x18 -> x, x19 -> x'}), NR: 'f(f(y,y'),f(x,x'))' ID: 12 => ('f(x',f(y',f(y,x)))', D2, R4, P[2], S{x17 -> y', x18 -> y, x19 -> x}), NR: 'f(y',f(y,x))' ID: 13 => ('f(x,f(y,f(y',x')))', D2, R1, P[], S{x8 -> x, x9 -> y, x10 -> f(y',x')}), NR: 'f(x,f(y,f(y',x')))' ID: 14 => ('f(y,f(x,f(y',x')))', D2, R2, P[], S{x11 -> y, x12 -> x, x13 -> f(y',x')}), NR: 'f(y,f(x,f(y',x')))' ID: 15 => ('f(y',f(x',f(x,y)))', D2, R3, P[], S{x14 -> y', x15 -> x', x16 -> f(x,y)}), NR: 'f(y',f(x',f(x,y)))' ID: 16 => ('f(y,f(f(x,y'),x'))', D2, R3, P[], S{x14 -> y, x15 -> f(x,y'), x16 -> x'}), NR: 'f(y,f(f(x,y'),x'))' ID: 17 => ('f(x',f(x,f(y',y)))', D2, R3, P[2], S{x14 -> x, x15 -> y', x16 -> y}), NR: 'f(x,f(y',y))' ID: 18 => ('f(f(x,y'),f(y,x'))', D2, R4, P[], S{x17 -> f(x,y'), x18 -> y, x19 -> x'}), NR: 'f(f(x,y'),f(y,x'))' ID: 19 => ('f(x,f(f(y,x'),y'))', D3, R3, P[], S{x14 -> x, x15 -> f(y,x'), x16 -> y'}), NR: 'f(x,f(f(y,x'),y'))' ID: 20 => ('f(y',f(y,f(x',x)))', D3, R3, P[2], S{x14 -> y, x15 -> x', x16 -> x}), NR: 'f(y,f(x',x))' ID: 21 => ('f(f(y,x'),f(x,y'))', D3, R4, P[], S{x17 -> f(y,x'), x18 -> x, x19 -> y'}), NR: 'f(f(y,x'),f(x,y'))' ID: 22 => ('f(y',f(x',f(y,x)))', D3, R4, P[2], S{x17 -> x', x18 -> y, x19 -> x}), NR: 'f(x',f(y,x))' ID: 23 => ('f(y,f(f(x,x'),y'))', D3, R3, P[], S{x14 -> y, x15 -> f(x,x'), x16 -> y'}), NR: 'f(y,f(f(x,x'),y'))' ID: 24 => ('f(y',f(x,f(x',y)))', D3, R3, P[2], S{x14 -> x, x15 -> x', x16 -> y}), NR: 'f(x,f(x',y))' ID: 25 => ('f(f(x,x'),f(y,y'))', D3, R4, P[], S{x17 -> f(x,x'), x18 -> y, x19 -> y'}), NR: 'f(f(x,x'),f(y,y'))' ID: 26 => ('f(x,f(y,f(x',y')))', D3, R1, P[], S{x8 -> x, x9 -> y, x10 -> f(x',y')}), NR: 'f(x,f(y,f(x',y')))' ID: 27 => ('f(y,f(x,f(x',y')))', D3, R2, P[], S{x11 -> y, x12 -> x, x13 -> f(x',y')}), NR: 'f(y,f(x,f(x',y')))' ID: 28 => ('f(x,f(y',f(y,x')))', D3, R2, P[2], S{x11 -> y', x12 -> y, x13 -> x'}), NR: 'f(y',f(y,x'))' ID: 29 => ('f(f(y,y'),f(x',x))', D3, R3, P[], S{x14 -> f(y,y'), x15 -> x', x16 -> x}), NR: 'f(f(y,y'),f(x',x))' ID: 30 => ('f(x',f(f(y,y'),x))', D3, R4, P[], S{x17 -> x', x18 -> f(y,y'), x19 -> x}), NR: 'f(x',f(f(y,y'),x))' ID: 31 => ('f(y,f(f(y',x),x'))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x), x16 -> x'}), NR: 'f(y,f(f(y',x),x'))' ID: 32 => ('f(f(y',x),f(y,x'))', D3, R4, P[], S{x17 -> f(y',x), x18 -> y, x19 -> x'}), NR: 'f(f(y',x),f(y,x'))' ID: 33 => ('f(y,f(y',f(x,x')))', D3, R1, P[], S{x8 -> y, x9 -> y', x10 -> f(x,x')}), NR: 'f(y,f(y',f(x,x')))' ID: 34 => ('f(x,f(x',f(y,y')))', D3, R3, P[], S{x14 -> x, x15 -> x', x16 -> f(y,y')}), NR: 'f(x,f(x',f(y,y')))' ID: 35 => ('f(y',f(f(y,x),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x), x16 -> x'}), NR: 'f(y',f(f(y,x),x'))' ID: 36 => ('f(f(y,x),f(y',x'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> y', x19 -> x'}), NR: 'f(f(y,x),f(y',x'))' ID: 37 => ('f(y,f(f(y',x'),x))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x'), x16 -> x}), NR: 'f(y,f(f(y',x'),x))' ID: 38 => ('f(x,f(y',f(x',y)))', D3, R3, P[2], S{x14 -> y', x15 -> x', x16 -> y}), NR: 'f(y',f(x',y))' ID: 39 => ('f(f(y',x'),f(y,x))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> y, x19 -> x}), NR: 'f(f(y',x'),f(y,x))' ID: 40 => ('f(x,f(x',f(y',y)))', D3, R4, P[2], S{x17 -> x', x18 -> y', x19 -> y}), NR: 'f(x',f(y',y))' ID: 41 => ('f(x,f(f(y',x'),y))', D3, R3, P[], S{x14 -> x, x15 -> f(y',x'), x16 -> y}), NR: 'f(x,f(f(y',x'),y))' ID: 42 => ('f(y,f(y',f(x',x)))', D3, R3, P[2], S{x14 -> y', x15 -> x', x16 -> x}), NR: 'f(y',f(x',x))' ID: 43 => ('f(f(y',x'),f(x,y))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> x, x19 -> y}), NR: 'f(f(y',x'),f(x,y))' ID: 44 => ('f(y,f(x',f(y',x)))', D3, R4, P[2], S{x17 -> x', x18 -> y', x19 -> x}), NR: 'f(x',f(y',x))' ID: 45 => ('f(f(x,y'),f(x',y))', D3, R3, P[], S{x14 -> f(x,y'), x15 -> x', x16 -> y}), NR: 'f(f(x,y'),f(x',y))' ID: 46 => ('f(x',f(f(x,y'),y))', D3, R4, P[], S{x17 -> x', x18 -> f(x,y'), x19 -> y}), NR: 'f(x',f(f(x,y'),y))' ID: 47 => ('f(x,f(f(y',y),x'))', D3, R3, P[], S{x14 -> x, x15 -> f(y',y), x16 -> x'}), NR: 'f(x,f(f(y',y),x'))' ID: 48 => ('f(f(y',y),f(x,x'))', D3, R4, P[], S{x17 -> f(y',y), x18 -> x, x19 -> x'}), NR: 'f(f(y',y),f(x,x'))' ID: 49 => ('f(y,f(x',f(x,y')))', D3, R3, P[], S{x14 -> y, x15 -> x', x16 -> f(x,y')}), NR: 'f(y,f(x',f(x,y')))' ID: 50 => ('f(f(y,x'),f(y',x))', D4, R3, P[], S{x14 -> f(y,x'), x15 -> y', x16 -> x}), NR: 'f(f(y,x'),f(y',x))' ID: 51 => ('f(y',f(f(y,x'),x))', D4, R4, P[], S{x17 -> y', x18 -> f(y,x'), x19 -> x}), NR: 'f(y',f(f(y,x'),x))' ID: 52 => ('f(y,f(f(x',x),y'))', D4, R3, P[], S{x14 -> y, x15 -> f(x',x), x16 -> y'}), NR: 'f(y,f(f(x',x),y'))' ID: 53 => ('f(f(x',x),f(y,y'))', D4, R4, P[], S{x17 -> f(x',x), x18 -> y, x19 -> y'}), NR: 'f(f(x',x),f(y,y'))' ID: 54 => ('f(x',f(f(y,x),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(y,x), x16 -> y'}), NR: 'f(x',f(f(y,x),y'))' ID: 55 => ('f(f(y,x),f(x',y'))', D4, R4, P[], S{x17 -> f(y,x), x18 -> x', x19 -> y'}), NR: 'f(f(y,x),f(x',y'))' ID: 56 => ('f(f(x,x'),f(y',y))', D4, R3, P[], S{x14 -> f(x,x'), x15 -> y', x16 -> y}), NR: 'f(f(x,x'),f(y',y))' ID: 57 => ('f(y',f(f(x,x'),y))', D4, R4, P[], S{x17 -> y', x18 -> f(x,x'), x19 -> y}), NR: 'f(y',f(f(x,x'),y))' ID: 58 => ('f(x,f(f(x',y),y'))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y), x16 -> y'}), NR: 'f(x,f(f(x',y),y'))' ID: 59 => ('f(f(x',y),f(x,y'))', D4, R4, P[], S{x17 -> f(x',y), x18 -> x, x19 -> y'}), NR: 'f(f(x',y),f(x,y'))' ID: 60 => ('f(y,f(f(x',y'),x))', D4, R3, P[], S{x14 -> y, x15 -> f(x',y'), x16 -> x}), NR: 'f(y,f(f(x',y'),x))' ID: 61 => ('f(f(x',y'),f(y,x))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> y, x19 -> x}), NR: 'f(f(x',y'),f(y,x))' ID: 62 => ('f(x,f(f(x',y'),y))', D4, R3, P[], S{x14 -> x, x15 -> f(x',y'), x16 -> y}), NR: 'f(x,f(f(x',y'),y))' ID: 63 => ('f(f(x',y'),f(x,y))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> x, x19 -> y}), NR: 'f(f(x',y'),f(x,y))' ID: 64 => ('f(f(y',x),f(x',y))', D4, R3, P[], S{x14 -> f(y',x), x15 -> x', x16 -> y}), NR: 'f(f(y',x),f(x',y))' ID: 65 => ('f(x',f(f(y',x),y))', D4, R4, P[], S{x17 -> x', x18 -> f(y',x), x19 -> y}), NR: 'f(x',f(f(y',x),y))' ID: 66 => ('f(y',f(f(x',y),x))', D4, R3, P[], S{x14 -> y', x15 -> f(x',y), x16 -> x}), NR: 'f(y',f(f(x',y),x))' ID: 67 => ('f(f(x',y),f(y',x))', D4, R4, P[], S{x17 -> f(x',y), x18 -> y', x19 -> x}), NR: 'f(f(x',y),f(y',x))' ID: 68 => ('f(x',f(f(y',y),x))', D4, R3, P[], S{x14 -> x', x15 -> f(y',y), x16 -> x}), NR: 'f(x',f(f(y',y),x))' ID: 69 => ('f(f(y',y),f(x',x))', D4, R4, P[], S{x17 -> f(y',y), x18 -> x', x19 -> x}), NR: 'f(f(y',y),f(x',x))' ID: 70 => ('f(y',f(f(x',x),y))', D4, R3, P[], S{x14 -> y', x15 -> f(x',x), x16 -> y}), NR: 'f(y',f(f(x',x),y))' ID: 71 => ('f(f(x',x),f(y',y))', D4, R4, P[], S{x17 -> f(x',x), x18 -> y', x19 -> y}), NR: 'f(f(x',x),f(y',y))' t: f(x,f(y,f(x',y'))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(x,f(y,f(x',y')))', D0) ID: 1 => ('f(y,f(f(x',y'),x))', D1, R3, P[], S{x14 -> y, x15 -> f(x',y'), x16 -> x}), NR: 'f(y,f(f(x',y'),x))' ID: 2 => ('f(x,f(x',f(y',y)))', D1, R3, P[2], S{x14 -> x', x15 -> y', x16 -> y}), NR: 'f(x',f(y',y))' ID: 3 => ('f(f(x',y'),f(y,x))', D1, R4, P[], S{x17 -> f(x',y'), x18 -> y, x19 -> x}), NR: 'f(f(x',y'),f(y,x))' ID: 4 => ('f(x,f(y',f(x',y)))', D1, R4, P[2], S{x17 -> y', x18 -> x', x19 -> y}), NR: 'f(y',f(x',y))' ID: 5 => ('f(y,f(x',f(y',x)))', D2, R1, P[2], S{x8 -> x', x9 -> y', x10 -> x}), NR: 'f(x',f(y',x))' ID: 6 => ('f(y,f(y',f(x',x)))', D2, R2, P[2], S{x11 -> y', x12 -> x', x13 -> x}), NR: 'f(y',f(x',x))' ID: 7 => ('f(f(x',y'),f(x,y))', D2, R3, P[], S{x14 -> f(x',y'), x15 -> x, x16 -> y}), NR: 'f(f(x',y'),f(x,y))' ID: 8 => ('f(x,f(f(x',y'),y))', D2, R4, P[], S{x17 -> x, x18 -> f(x',y'), x19 -> y}), NR: 'f(x,f(f(x',y'),y))' ID: 9 => ('f(x',f(f(y',y),x))', D2, R3, P[], S{x14 -> x', x15 -> f(y',y), x16 -> x}), NR: 'f(x',f(f(y',y),x))' ID: 10 => ('f(x,f(y',f(y,x')))', D2, R3, P[2], S{x14 -> y', x15 -> y, x16 -> x'}), NR: 'f(y',f(y,x'))' ID: 11 => ('f(f(y',y),f(x',x))', D2, R4, P[], S{x17 -> f(y',y), x18 -> x', x19 -> x}), NR: 'f(f(y',y),f(x',x))' ID: 12 => ('f(x,f(y,f(y',x')))', D2, R4, P[2], S{x17 -> y, x18 -> y', x19 -> x'}), NR: 'f(y,f(y',x'))' ID: 13 => ('f(x',f(y',f(y,x)))', D2, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(y,x)}), NR: 'f(x',f(y',f(y,x)))' ID: 14 => ('f(y',f(x',f(y,x)))', D2, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(y,x)}), NR: 'f(y',f(x',f(y,x)))' ID: 15 => ('f(y,f(x,f(x',y')))', D2, R3, P[], S{x14 -> y, x15 -> x, x16 -> f(x',y')}), NR: 'f(y,f(x,f(x',y')))' ID: 16 => ('f(y',f(f(x',y),x))', D2, R3, P[], S{x14 -> y', x15 -> f(x',y), x16 -> x}), NR: 'f(y',f(f(x',y),x))' ID: 17 => ('f(x,f(x',f(y,y')))', D2, R3, P[2], S{x14 -> x', x15 -> y, x16 -> y'}), NR: 'f(x',f(y,y'))' ID: 18 => ('f(f(x',y),f(y',x))', D2, R4, P[], S{x17 -> f(x',y), x18 -> y', x19 -> x}), NR: 'f(f(x',y),f(y',x))' ID: 19 => ('f(x',f(f(y',x),y))', D3, R3, P[], S{x14 -> x', x15 -> f(y',x), x16 -> y}), NR: 'f(x',f(f(y',x),y))' ID: 20 => ('f(y,f(y',f(x,x')))', D3, R3, P[2], S{x14 -> y', x15 -> x, x16 -> x'}), NR: 'f(y',f(x,x'))' ID: 21 => ('f(f(y',x),f(x',y))', D3, R4, P[], S{x17 -> f(y',x), x18 -> x', x19 -> y}), NR: 'f(f(y',x),f(x',y))' ID: 22 => ('f(y,f(x,f(y',x')))', D3, R4, P[2], S{x17 -> x, x18 -> y', x19 -> x'}), NR: 'f(x,f(y',x'))' ID: 23 => ('f(y',f(f(x',x),y))', D3, R3, P[], S{x14 -> y', x15 -> f(x',x), x16 -> y}), NR: 'f(y',f(f(x',x),y))' ID: 24 => ('f(y,f(x',f(x,y')))', D3, R3, P[2], S{x14 -> x', x15 -> x, x16 -> y'}), NR: 'f(x',f(x,y'))' ID: 25 => ('f(f(x',x),f(y',y))', D3, R4, P[], S{x17 -> f(x',x), x18 -> y', x19 -> y}), NR: 'f(f(x',x),f(y',y))' ID: 26 => ('f(x',f(y',f(x,y)))', D3, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(x,y)}), NR: 'f(x',f(y',f(x,y)))' ID: 27 => ('f(y',f(x',f(x,y)))', D3, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(x,y)}), NR: 'f(y',f(x',f(x,y)))' ID: 28 => ('f(x',f(y,f(y',x)))', D3, R2, P[2], S{x11 -> y, x12 -> y', x13 -> x}), NR: 'f(y,f(y',x))' ID: 29 => ('f(f(y',y),f(x,x'))', D3, R3, P[], S{x14 -> f(y',y), x15 -> x, x16 -> x'}), NR: 'f(f(y',y),f(x,x'))' ID: 30 => ('f(x,f(f(y',y),x'))', D3, R4, P[], S{x17 -> x, x18 -> f(y',y), x19 -> x'}), NR: 'f(x,f(f(y',y),x'))' ID: 31 => ('f(y',f(f(y,x'),x))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x'), x16 -> x}), NR: 'f(y',f(f(y,x'),x))' ID: 32 => ('f(f(y,x'),f(y',x))', D3, R4, P[], S{x17 -> f(y,x'), x18 -> y', x19 -> x}), NR: 'f(f(y,x'),f(y',x))' ID: 33 => ('f(y',f(y,f(x',x)))', D3, R1, P[], S{x8 -> y', x9 -> y, x10 -> f(x',x)}), NR: 'f(y',f(y,f(x',x)))' ID: 34 => ('f(x',f(x,f(y',y)))', D3, R3, P[], S{x14 -> x', x15 -> x, x16 -> f(y',y)}), NR: 'f(x',f(x,f(y',y)))' ID: 35 => ('f(y,f(f(y',x'),x))', D3, R3, P[], S{x14 -> y, x15 -> f(y',x'), x16 -> x}), NR: 'f(y,f(f(y',x'),x))' ID: 36 => ('f(f(y',x'),f(y,x))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> y, x19 -> x}), NR: 'f(f(y',x'),f(y,x))' ID: 37 => ('f(y',f(f(y,x),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(y,x), x16 -> x'}), NR: 'f(y',f(f(y,x),x'))' ID: 38 => ('f(x',f(y,f(x,y')))', D3, R3, P[2], S{x14 -> y, x15 -> x, x16 -> y'}), NR: 'f(y,f(x,y'))' ID: 39 => ('f(f(y,x),f(y',x'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> y', x19 -> x'}), NR: 'f(f(y,x),f(y',x'))' ID: 40 => ('f(x',f(x,f(y,y')))', D3, R4, P[2], S{x17 -> x, x18 -> y, x19 -> y'}), NR: 'f(x,f(y,y'))' ID: 41 => ('f(x',f(f(y,x),y'))', D3, R3, P[], S{x14 -> x', x15 -> f(y,x), x16 -> y'}), NR: 'f(x',f(f(y,x),y'))' ID: 42 => ('f(y',f(y,f(x,x')))', D3, R3, P[2], S{x14 -> y, x15 -> x, x16 -> x'}), NR: 'f(y,f(x,x'))' ID: 43 => ('f(f(y,x),f(x',y'))', D3, R4, P[], S{x17 -> f(y,x), x18 -> x', x19 -> y'}), NR: 'f(f(y,x),f(x',y'))' ID: 44 => ('f(y',f(x,f(y,x')))', D3, R4, P[2], S{x17 -> x, x18 -> y, x19 -> x'}), NR: 'f(x,f(y,x'))' ID: 45 => ('f(f(x',y),f(x,y'))', D3, R3, P[], S{x14 -> f(x',y), x15 -> x, x16 -> y'}), NR: 'f(f(x',y),f(x,y'))' ID: 46 => ('f(x,f(f(x',y),y'))', D3, R4, P[], S{x17 -> x, x18 -> f(x',y), x19 -> y'}), NR: 'f(x,f(f(x',y),y'))' ID: 47 => ('f(x',f(f(y,y'),x))', D3, R3, P[], S{x14 -> x', x15 -> f(y,y'), x16 -> x}), NR: 'f(x',f(f(y,y'),x))' ID: 48 => ('f(f(y,y'),f(x',x))', D3, R4, P[], S{x17 -> f(y,y'), x18 -> x', x19 -> x}), NR: 'f(f(y,y'),f(x',x))' ID: 49 => ('f(y',f(x,f(x',y)))', D3, R3, P[], S{x14 -> y', x15 -> x, x16 -> f(x',y)}), NR: 'f(y',f(x,f(x',y)))' ID: 50 => ('f(f(y',x),f(y,x'))', D4, R3, P[], S{x14 -> f(y',x), x15 -> y, x16 -> x'}), NR: 'f(f(y',x),f(y,x'))' ID: 51 => ('f(y,f(f(y',x),x'))', D4, R4, P[], S{x17 -> y, x18 -> f(y',x), x19 -> x'}), NR: 'f(y,f(f(y',x),x'))' ID: 52 => ('f(y',f(f(x,x'),y))', D4, R3, P[], S{x14 -> y', x15 -> f(x,x'), x16 -> y}), NR: 'f(y',f(f(x,x'),y))' ID: 53 => ('f(f(x,x'),f(y',y))', D4, R4, P[], S{x17 -> f(x,x'), x18 -> y', x19 -> y}), NR: 'f(f(x,x'),f(y',y))' ID: 54 => ('f(x,f(f(y',x'),y))', D4, R3, P[], S{x14 -> x, x15 -> f(y',x'), x16 -> y}), NR: 'f(x,f(f(y',x'),y))' ID: 55 => ('f(f(y',x'),f(x,y))', D4, R4, P[], S{x17 -> f(y',x'), x18 -> x, x19 -> y}), NR: 'f(f(y',x'),f(x,y))' ID: 56 => ('f(f(x',x),f(y,y'))', D4, R3, P[], S{x14 -> f(x',x), x15 -> y, x16 -> y'}), NR: 'f(f(x',x),f(y,y'))' ID: 57 => ('f(y,f(f(x',x),y'))', D4, R4, P[], S{x17 -> y, x18 -> f(x',x), x19 -> y'}), NR: 'f(y,f(f(x',x),y'))' ID: 58 => ('f(x',f(f(x,y'),y))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y'), x16 -> y}), NR: 'f(x',f(f(x,y'),y))' ID: 59 => ('f(f(x,y'),f(x',y))', D4, R4, P[], S{x17 -> f(x,y'), x18 -> x', x19 -> y}), NR: 'f(f(x,y'),f(x',y))' ID: 60 => ('f(y',f(f(x,y),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(x,y), x16 -> x'}), NR: 'f(y',f(f(x,y),x'))' ID: 61 => ('f(f(x,y),f(y',x'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> y', x19 -> x'}), NR: 'f(f(x,y),f(y',x'))' ID: 62 => ('f(x',f(f(x,y),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(x,y), x16 -> y'}), NR: 'f(x',f(f(x,y),y'))' ID: 63 => ('f(f(x,y),f(x',y'))', D4, R4, P[], S{x17 -> f(x,y), x18 -> x', x19 -> y'}), NR: 'f(f(x,y),f(x',y'))' ID: 64 => ('f(f(y,x'),f(x,y'))', D4, R3, P[], S{x14 -> f(y,x'), x15 -> x, x16 -> y'}), NR: 'f(f(y,x'),f(x,y'))' ID: 65 => ('f(x,f(f(y,x'),y'))', D4, R4, P[], S{x17 -> x, x18 -> f(y,x'), x19 -> y'}), NR: 'f(x,f(f(y,x'),y'))' ID: 66 => ('f(y,f(f(x,y'),x'))', D4, R3, P[], S{x14 -> y, x15 -> f(x,y'), x16 -> x'}), NR: 'f(y,f(f(x,y'),x'))' ID: 67 => ('f(f(x,y'),f(y,x'))', D4, R4, P[], S{x17 -> f(x,y'), x18 -> y, x19 -> x'}), NR: 'f(f(x,y'),f(y,x'))' ID: 68 => ('f(x,f(f(y,y'),x'))', D4, R3, P[], S{x14 -> x, x15 -> f(y,y'), x16 -> x'}), NR: 'f(x,f(f(y,y'),x'))' ID: 69 => ('f(f(y,y'),f(x,x'))', D4, R4, P[], S{x17 -> f(y,y'), x18 -> x, x19 -> x'}), NR: 'f(f(y,y'),f(x,x'))' ID: 70 => ('f(y,f(f(x,x'),y'))', D4, R3, P[], S{x14 -> y, x15 -> f(x,x'), x16 -> y'}), NR: 'f(y,f(f(x,x'),y'))' ID: 71 => ('f(f(x,x'),f(y,y'))', D4, R4, P[], S{x17 -> f(x,x'), x18 -> y, x19 -> y'}), NR: 'f(f(x,x'),f(y,y'))' SNodesPath1: f(x',f(y',f(x,y))) TNodesPath1: f(x,f(y,f(x',y'))) -> f(y,f(f(x',y'),x)) -> f(y,f(x',f(y',x))) -> f(x',f(f(y',x),y)) -> f(x',f(y',f(x,y))) SNodesPath2: f(x',f(y',f(x,y))) -> f(y',f(f(x,y),x')) -> f(y',f(x,f(y,x'))) -> f(x,f(f(y,x'),y')) -> f(x,f(y,f(x',y'))) TNodesPath2: f(x,f(y,f(x',y'))) f(x',f(y',f(x,y))) ->= f(x',f(y',f(x,y))) *<- f(x,f(y,f(x',y'))) f(x,f(y,f(x',y'))) ->= f(x,f(y,f(x',y'))) *<- f(x',f(y',f(x,y))) "Strongly closed critical pair" The problem is confluent. Problem 1.7: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Not overlay, Proper, NW0, N15 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(f(x',f(y',z')),z) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,13),(3,14),(3,15),(3,16),(4,0),(4,17),(4,18),(4,19),(5,20),(5,21),(5,22),(5,23),(6,11),(6,24),(6,25),(6,26),(7,11),(7,12),(7,27),(7,28),(8,1),(8,2),(8,29),(8,30),(9,31),(9,32),(9,33),(9,34),(10,35),(10,36),(10,37),(10,38),(11,5),(11,6),(11,7),(11,8),(12,1),(12,2),(12,29),(12,30),(13,9),(13,39),(13,40),(13,41),(14,6),(14,29),(14,42),(14,43),(15,0),(15,19),(15,44),(15,45),(16,3),(16,4),(16,46),(16,47),(17,10),(17,42),(17,48),(17,49),(18,5),(18,30),(18,39),(18,50),(19,15),(19,16),(19,51),(19,52),(20,27),(20,43),(20,53),(20,54),(21,11),(21,25),(21,55),(21,56),(22,5),(22,30),(22,39),(22,50),(23,5),(23,6),(23,57),(23,58),(24,28),(24,50),(24,59),(24,60),(25,21),(25,23),(25,61),(25,62),(26,6),(26,29),(26,42),(26,43),(27,32),(27,34),(27,63),(27,64),(28,36),(28,38),(28,65),(28,66),(29,13),(29,14),(29,67),(29,68),(30,12),(30,17),(30,18),(30,69),(31,35),(31,36),(31,37),(31,38),(32,27),(32,43),(32,70),(32,71),(33,9),(33,10),(33,23),(33,68),(34,9),(34,39),(34,72),(34,73),(35,31),(35,32),(35,33),(35,34),(36,28),(36,50),(36,74),(36,75),(37,9),(37,10),(37,11),(37,12),(38,10),(38,42),(38,76),(38,77),(39,27),(39,43),(39,53),(39,54),(40,21),(40,29),(40,36),(40,43),(41,13),(41,14),(41,67),(41,68),(42,28),(42,50),(42,59),(42,60),(43,9),(43,39),(43,40),(43,41),(44,10),(44,42),(44,76),(44,77),(45,5),(45,38),(45,39),(45,67),(46,5),(46,6),(46,57),(46,58),(47,9),(47,10),(47,23),(47,68),(48,25),(48,30),(48,32),(48,50),(49,12),(49,17),(49,18),(49,69),(50,10),(50,42),(50,48),(50,49),(51,9),(51,39),(51,72),(51,73),(52,6),(52,34),(52,42),(52,69),(53,5),(53,38),(53,39),(53,67),(54,20),(54,21),(54,22),(54,23),(55,28),(55,50),(55,74),(55,75),(56,21),(56,29),(56,36),(56,43),(57,29),(57,30),(57,46),(57,47),(58,23),(58,27),(58,28),(58,68),(59,6),(59,34),(59,42),(59,69),(60,11),(60,24),(60,25),(60,26),(61,27),(61,43),(61,70),(61,71),(62,25),(62,30),(62,32),(62,50),(63,36),(63,38),(63,65),(63,66),(64,23),(64,27),(64,28),(64,68),(65,32),(65,34),(65,63),(65,64),(66,11),(66,12),(66,27),(66,28),(67,12),(67,44),(67,45),(67,69),(68,29),(68,30),(68,46),(68,47),(69,51),(69,52),(69,67),(69,68),(70,21),(70,23),(70,61),(70,62),(71,25),(71,32),(71,38),(71,67),(72,51),(72,52),(72,67),(72,68),(73,21),(73,34),(73,36),(73,69),(74,11),(74,25),(74,55),(74,56),(75,21),(75,34),(75,36),(75,69),(76,12),(76,44),(76,45),(76,69),(77,25),(77,32),(77,38),(77,67)] ID: 0 => ('f(f(x',f(y',z')),z)', D0) ID: 1 => ('f(x',f(f(y',z'),z))', D1, R1, P[], S{x8 -> x', x9 -> f(y',z'), x10 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 2 => ('f(f(y',z'),f(x',z))', D1, R2, P[], S{x11 -> f(y',z'), x12 -> x', x13 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 3 => ('f(f(y',f(z',x')),z)', D1, R3, P[1], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 4 => ('f(f(z',f(y',x')),z)', D1, R4, P[1], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 5 => ('f(x',f(y',f(z',z)))', D2, R1, P[2], S{x8 -> y', x9 -> z', x10 -> z}), NR: 'f(y',f(z',z))' ID: 6 => ('f(x',f(z',f(y',z)))', D2, R2, P[2], S{x11 -> z', x12 -> y', x13 -> z}), NR: 'f(z',f(y',z))' ID: 7 => ('f(f(y',z'),f(z,x'))', D2, R3, P[], S{x14 -> f(y',z'), x15 -> z, x16 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 8 => ('f(z,f(f(y',z'),x'))', D2, R4, P[], S{x17 -> z, x18 -> f(y',z'), x19 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 9 => ('f(y',f(z',f(x',z)))', D2, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 10 => ('f(z',f(y',f(x',z)))', D2, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(x',z)}), NR: 'f(z',f(y',f(x',z)))' ID: 11 => ('f(x',f(z,f(y',z')))', D2, R3, P[], S{x14 -> x', x15 -> z, x16 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 12 => ('f(z,f(x',f(y',z')))', D2, R4, P[], S{x17 -> z, x18 -> x', x19 -> f(y',z')}), NR: 'f(z,f(x',f(y',z')))' ID: 13 => ('f(y',f(f(z',x'),z))', D2, R1, P[], S{x8 -> y', x9 -> f(z',x'), x10 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 14 => ('f(f(z',x'),f(y',z))', D2, R2, P[], S{x11 -> f(z',x'), x12 -> y', x13 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 15 => ('f(f(z',f(x',y')),z)', D2, R3, P[1], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 16 => ('f(f(x',f(z',y')),z)', D2, R4, P[1], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 17 => ('f(z',f(f(y',x'),z))', D2, R1, P[], S{x8 -> z', x9 -> f(y',x'), x10 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R2, P[], S{x11 -> f(y',x'), x12 -> z', x13 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(f(y',f(x',z')),z)', D2, R3, P[1], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 20 => ('f(y',f(f(z',z),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 21 => ('f(x',f(z',f(z,y')))', D3, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 22 => ('f(f(z',z),f(y',x'))', D3, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 23 => ('f(x',f(z,f(z',y')))', D3, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 24 => ('f(z',f(f(y',z),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 25 => ('f(x',f(y',f(z,z')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> z'}), NR: 'f(y',f(z,z'))' ID: 26 => ('f(f(y',z),f(z',x'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 27 => ('f(y',f(z',f(z,x')))', D3, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(z,x')}), NR: 'f(y',f(z',f(z,x')))' ID: 28 => ('f(z',f(y',f(z,x')))', D3, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(z,x')}), NR: 'f(z',f(y',f(z,x')))' ID: 29 => ('f(z,f(y',f(z',x')))', D3, R1, P[2], S{x8 -> y', x9 -> z', x10 -> x'}), NR: 'f(y',f(z',x'))' ID: 30 => ('f(z,f(z',f(y',x')))', D3, R2, P[2], S{x11 -> z', x12 -> y', x13 -> x'}), NR: 'f(z',f(y',x'))' ID: 31 => ('f(z',f(f(x',z),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 32 => ('f(y',f(x',f(z,z')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> z'}), NR: 'f(x',f(z,z'))' ID: 33 => ('f(f(x',z),f(z',y'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 34 => ('f(y',f(z,f(x',z')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> z'}), NR: 'f(z,f(x',z'))' ID: 35 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 36 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 37 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 38 => ('f(z',f(z,f(x',y')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 39 => ('f(y',f(x',f(z',z)))', D3, R2, P[2], S{x11 -> x', x12 -> z', x13 -> z}), NR: 'f(x',f(z',z))' ID: 40 => ('f(f(z',x'),f(z,y'))', D3, R3, P[], S{x14 -> f(z',x'), x15 -> z, x16 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 41 => ('f(z,f(f(z',x'),y'))', D3, R4, P[], S{x17 -> z, x18 -> f(z',x'), x19 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 42 => ('f(z',f(x',f(y',z)))', D3, R1, P[], S{x8 -> z', x9 -> x', x10 -> f(y',z)}), NR: 'f(z',f(x',f(y',z)))' ID: 43 => ('f(y',f(z,f(z',x')))', D3, R3, P[], S{x14 -> y', x15 -> z, x16 -> f(z',x')}), NR: 'f(y',f(z,f(z',x')))' ID: 44 => ('f(z',f(f(x',y'),z))', D3, R1, P[], S{x8 -> z', x9 -> f(x',y'), x10 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 45 => ('f(f(x',y'),f(z',z))', D3, R2, P[], S{x11 -> f(x',y'), x12 -> z', x13 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 46 => ('f(x',f(f(z',y'),z))', D3, R1, P[], S{x8 -> x', x9 -> f(z',y'), x10 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 47 => ('f(f(z',y'),f(x',z))', D3, R2, P[], S{x11 -> f(z',y'), x12 -> x', x13 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 48 => ('f(f(y',x'),f(z,z'))', D3, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 49 => ('f(z,f(f(y',x'),z'))', D3, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 50 => ('f(z',f(z,f(y',x')))', D3, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 51 => ('f(y',f(f(x',z'),z))', D3, R1, P[], S{x8 -> y', x9 -> f(x',z'), x10 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 52 => ('f(f(x',z'),f(y',z))', D3, R2, P[], S{x11 -> f(x',z'), x12 -> y', x13 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 53 => ('f(f(z',z),f(x',y'))', D4, R3, P[], S{x14 -> f(z',z), x15 -> x', x16 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 54 => ('f(x',f(f(z',z),y'))', D4, R4, P[], S{x17 -> x', x18 -> f(z',z), x19 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 55 => ('f(z',f(f(z,y'),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 56 => ('f(f(z,y'),f(z',x'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 57 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 58 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 59 => ('f(f(y',z),f(x',z'))', D4, R3, P[], S{x14 -> f(y',z), x15 -> x', x16 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 60 => ('f(x',f(f(y',z),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(y',z), x19 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 61 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 62 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 63 => ('f(z',f(f(z,x'),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 64 => ('f(f(z,x'),f(z',y'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 65 => ('f(y',f(f(z,x'),z'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 66 => ('f(f(z,x'),f(y',z'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 67 => ('f(z,f(z',f(x',y')))', D4, R3, P[2], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 68 => ('f(z,f(x',f(z',y')))', D4, R4, P[2], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 69 => ('f(z,f(y',f(x',z')))', D4, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 70 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 71 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 72 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 73 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 74 => ('f(x',f(f(z,y'),z'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 75 => ('f(f(z,y'),f(x',z'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 76 => ('f(z,f(f(x',y'),z'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 77 => ('f(f(x',y'),f(z,z'))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' t: f(f(y',x'),f(z',z)) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,13),(3,14),(3,15),(3,16),(4,0),(4,17),(4,18),(4,19),(5,9),(5,10),(5,11),(5,12),(6,20),(6,21),(6,22),(6,23),(7,1),(7,2),(7,24),(7,25),(8,1),(8,26),(8,27),(8,28),(9,5),(9,6),(9,7),(9,8),(10,29),(10,30),(10,31),(10,32),(11,1),(11,2),(11,3),(11,4),(12,2),(12,33),(12,34),(12,35),(13,0),(13,17),(13,18),(13,19),(14,24),(14,36),(14,37),(14,38),(15,3),(15,4),(15,23),(15,32),(16,3),(16,39),(16,40),(16,41),(17,13),(17,14),(17,15),(17,16),(18,25),(18,42),(18,43),(18,44),(19,4),(19,45),(19,46),(19,47),(20,24),(20,37),(20,48),(20,49),(21,1),(21,27),(21,50),(21,51),(22,6),(22,12),(22,40),(22,43),(23,6),(23,8),(23,52),(23,53),(24,14),(24,16),(24,54),(24,55),(25,18),(25,19),(25,56),(25,57),(26,25),(26,43),(26,58),(26,59),(27,21),(27,23),(27,60),(27,61),(28,8),(28,10),(28,37),(28,46),(29,3),(29,40),(29,62),(29,63),(30,2),(30,34),(30,64),(30,65),(31,8),(31,10),(31,37),(31,46),(32,10),(32,12),(32,66),(32,67),(33,4),(33,46),(33,68),(33,69),(34,30),(34,32),(34,70),(34,71),(35,6),(35,12),(35,40),(35,43),(36,21),(36,23),(36,60),(36,61),(37,3),(37,40),(37,62),(37,63),(38,14),(38,19),(38,27),(38,30),(39,30),(39,32),(39,70),(39,71),(40,24),(40,37),(40,48),(40,49),(41,16),(41,18),(41,21),(41,34),(42,1),(42,27),(42,50),(42,51),(43,4),(43,46),(43,68),(43,69),(44,16),(44,18),(44,21),(44,34),(45,2),(45,34),(45,64),(45,65),(46,25),(46,43),(46,58),(46,59),(47,14),(47,19),(47,27),(47,30),(48,6),(48,19),(48,30),(48,40),(49,20),(49,21),(49,22),(49,23),(50,25),(50,42),(50,43),(50,44),(51,10),(51,18),(51,21),(51,37),(52,10),(52,12),(52,66),(52,67),(53,23),(53,24),(53,25),(53,32),(54,18),(54,19),(54,56),(54,57),(55,23),(55,24),(55,25),(55,32),(56,14),(56,16),(56,54),(56,55),(57,1),(57,2),(57,24),(57,25),(58,8),(58,16),(58,34),(58,46),(59,1),(59,26),(59,27),(59,28),(60,24),(60,36),(60,37),(60,38),(61,12),(61,14),(61,27),(61,43),(62,10),(62,18),(62,21),(62,37),(63,29),(63,30),(63,31),(63,32),(64,4),(64,45),(64,46),(64,47),(65,6),(65,19),(65,30),(65,40),(66,6),(66,8),(66,52),(66,53),(67,3),(67,4),(67,23),(67,32),(68,12),(68,14),(68,27),(68,43),(69,2),(69,33),(69,34),(69,35),(70,3),(70,39),(70,40),(70,41),(71,8),(71,16),(71,34),(71,46)] ID: 0 => ('f(f(y',x'),f(z',z))', D0) ID: 1 => ('f(y',f(x',f(z',z)))', D1, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(z',z)}), NR: 'f(y',f(x',f(z',z)))' ID: 2 => ('f(x',f(y',f(z',z)))', D1, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(z',z)}), NR: 'f(x',f(y',f(z',z)))' ID: 3 => ('f(z',f(z,f(y',x')))', D1, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 4 => ('f(z,f(z',f(y',x')))', D1, R4, P[], S{x17 -> z, x18 -> z', x19 -> f(y',x')}), NR: 'f(z,f(z',f(y',x')))' ID: 5 => ('f(x',f(f(z',z),y'))', D2, R3, P[], S{x14 -> x', x15 -> f(z',z), x16 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 6 => ('f(y',f(z',f(z,x')))', D2, R3, P[2], S{x14 -> z', x15 -> z, x16 -> x'}), NR: 'f(z',f(z,x'))' ID: 7 => ('f(f(z',z),f(x',y'))', D2, R4, P[], S{x17 -> f(z',z), x18 -> x', x19 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 8 => ('f(y',f(z,f(z',x')))', D2, R4, P[2], S{x17 -> z, x18 -> z', x19 -> x'}), NR: 'f(z,f(z',x'))' ID: 9 => ('f(y',f(f(z',z),x'))', D2, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 10 => ('f(x',f(z',f(z,y')))', D2, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 11 => ('f(f(z',z),f(y',x'))', D2, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 12 => ('f(x',f(z,f(z',y')))', D2, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 13 => ('f(z,f(f(y',x'),z'))', D2, R3, P[], S{x14 -> z, x15 -> f(y',x'), x16 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 14 => ('f(z',f(y',f(x',z)))', D2, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z}), NR: 'f(y',f(x',z))' ID: 15 => ('f(f(y',x'),f(z,z'))', D2, R4, P[], S{x17 -> f(y',x'), x18 -> z, x19 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 16 => ('f(z',f(x',f(y',z)))', D2, R4, P[2], S{x17 -> x', x18 -> y', x19 -> z}), NR: 'f(x',f(y',z))' ID: 17 => ('f(z',f(f(y',x'),z))', D2, R3, P[], S{x14 -> z', x15 -> f(y',x'), x16 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 18 => ('f(z,f(y',f(x',z')))', D2, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 19 => ('f(z,f(x',f(y',z')))', D2, R4, P[2], S{x17 -> x', x18 -> y', x19 -> z'}), NR: 'f(x',f(y',z'))' ID: 20 => ('f(z',f(f(z,x'),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 21 => ('f(y',f(z,f(x',z')))', D3, R3, P[2], S{x14 -> z, x15 -> x', x16 -> z'}), NR: 'f(z,f(x',z'))' ID: 22 => ('f(f(z,x'),f(z',y'))', D3, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 23 => ('f(y',f(x',f(z,z')))', D3, R4, P[2], S{x17 -> x', x18 -> z, x19 -> z'}), NR: 'f(x',f(z,z'))' ID: 24 => ('f(z',f(z,f(x',y')))', D3, R1, P[], S{x8 -> z', x9 -> z, x10 -> f(x',y')}), NR: 'f(z',f(z,f(x',y')))' ID: 25 => ('f(z,f(z',f(x',y')))', D3, R2, P[], S{x11 -> z, x12 -> z', x13 -> f(x',y')}), NR: 'f(z,f(z',f(x',y')))' ID: 26 => ('f(z,f(f(z',x'),y'))', D3, R3, P[], S{x14 -> z, x15 -> f(z',x'), x16 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 27 => ('f(y',f(z',f(x',z)))', D3, R3, P[2], S{x14 -> z', x15 -> x', x16 -> z}), NR: 'f(z',f(x',z))' ID: 28 => ('f(f(z',x'),f(z,y'))', D3, R4, P[], S{x17 -> f(z',x'), x18 -> z, x19 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 29 => ('f(z',f(f(z,y'),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 30 => ('f(x',f(z,f(y',z')))', D3, R3, P[2], S{x14 -> z, x15 -> y', x16 -> z'}), NR: 'f(z,f(y',z'))' ID: 31 => ('f(f(z,y'),f(z',x'))', D3, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 32 => ('f(x',f(y',f(z,z')))', D3, R4, P[2], S{x17 -> y', x18 -> z, x19 -> z'}), NR: 'f(y',f(z,z'))' ID: 33 => ('f(z,f(f(z',y'),x'))', D3, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 34 => ('f(x',f(z',f(y',z)))', D3, R3, P[2], S{x14 -> z', x15 -> y', x16 -> z}), NR: 'f(z',f(y',z))' ID: 35 => ('f(f(z',y'),f(z,x'))', D3, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 36 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 37 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 38 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 39 => ('f(x',f(f(y',z),z'))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z), x16 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 40 => ('f(z',f(y',f(z,x')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> x'}), NR: 'f(y',f(z,x'))' ID: 41 => ('f(f(y',z),f(x',z'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> x', x19 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 42 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 43 => ('f(z,f(x',f(z',y')))', D3, R3, P[2], S{x14 -> x', x15 -> z', x16 -> y'}), NR: 'f(x',f(z',y'))' ID: 44 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 45 => ('f(x',f(f(y',z'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 46 => ('f(z,f(y',f(z',x')))', D3, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 47 => ('f(f(y',z'),f(x',z))', D3, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 48 => ('f(f(z,x'),f(y',z'))', D4, R3, P[], S{x14 -> f(z,x'), x15 -> y', x16 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 49 => ('f(y',f(f(z,x'),z'))', D4, R4, P[], S{x17 -> y', x18 -> f(z,x'), x19 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 50 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 51 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 52 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 53 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 54 => ('f(z,f(f(x',y'),z'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 55 => ('f(f(x',y'),f(z,z'))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 56 => ('f(z',f(f(x',y'),z))', D4, R3, P[], S{x14 -> z', x15 -> f(x',y'), x16 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 57 => ('f(f(x',y'),f(z',z))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> z', x19 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 58 => ('f(f(z',x'),f(y',z))', D4, R3, P[], S{x14 -> f(z',x'), x15 -> y', x16 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 59 => ('f(y',f(f(z',x'),z))', D4, R4, P[], S{x17 -> y', x18 -> f(z',x'), x19 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 60 => ('f(z',f(f(x',z),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 61 => ('f(f(x',z),f(z',y'))', D4, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 62 => ('f(f(z,y'),f(x',z'))', D4, R3, P[], S{x14 -> f(z,y'), x15 -> x', x16 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 63 => ('f(x',f(f(z,y'),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(z,y'), x19 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 64 => ('f(z,f(f(y',z'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',z'), x16 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 65 => ('f(f(y',z'),f(z,x'))', D4, R4, P[], S{x17 -> f(y',z'), x18 -> z, x19 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 66 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 67 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 68 => ('f(f(z',y'),f(x',z))', D4, R3, P[], S{x14 -> f(z',y'), x15 -> x', x16 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 69 => ('f(x',f(f(z',y'),z))', D4, R4, P[], S{x17 -> x', x18 -> f(z',y'), x19 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 70 => ('f(z',f(f(y',z),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 71 => ('f(f(y',z),f(z',x'))', D4, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' SNodesPath1: f(f(x',f(y',z')),z) -> f(x',f(f(y',z'),z)) TNodesPath1: f(f(y',x'),f(z',z)) -> f(y',f(x',f(z',z))) -> f(x',f(f(z',z),y')) -> f(y',f(f(z',z),x')) -> f(y',f(z',f(z,x'))) -> f(z',f(f(z,x'),y')) -> f(z',f(z,f(x',y'))) -> f(z',f(y',f(x',z))) -> f(y',f(f(x',z),z')) -> f(y',f(z,f(x',z'))) -> f(y',f(z',f(x',z))) -> f(y',f(x',f(z,z'))) -> f(y',f(z,f(z',x'))) -> f(z,f(f(z',x'),y')) -> f(z,f(z',f(x',y'))) -> f(z,f(y',f(x',z'))) -> f(y',f(f(x',z'),z)) -> f(z,f(f(x',z'),y')) -> f(z,f(x',f(z',y'))) -> f(z,f(z',f(y',x'))) -> f(z',f(f(y',x'),z)) -> f(z,f(f(y',x'),z')) -> f(z,f(x',f(y',z'))) -> f(x',f(f(y',z'),z)) SNodesPath2: TNodesPath2: f(f(y',x'),f(z',z)) f(f(x',f(y',z')),z) ->= f(x',f(f(y',z'),z)) *<- f(f(y',x'),f(z',z)) f(f(y',x'),f(z',z)) ->= f(f(y',x'),f(z',z)) *<- f(f(x',f(y',z')),z) "Strongly closed critical pair" The problem is confluent. Problem 1.8: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Not overlay, Proper, NW0, N16 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(z,f(x',f(y',z'))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(z,f(x',f(y',z')))', D0) ID: 1 => ('f(x',f(f(y',z'),z))', D1, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 2 => ('f(z,f(y',f(z',x')))', D1, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 3 => ('f(f(y',z'),f(x',z))', D1, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 4 => ('f(z,f(z',f(y',x')))', D1, R4, P[2], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 5 => ('f(x',f(y',f(z',z)))', D2, R1, P[2], S{x8 -> y', x9 -> z', x10 -> z}), NR: 'f(y',f(z',z))' ID: 6 => ('f(x',f(z',f(y',z)))', D2, R2, P[2], S{x11 -> z', x12 -> y', x13 -> z}), NR: 'f(z',f(y',z))' ID: 7 => ('f(f(y',z'),f(z,x'))', D2, R3, P[], S{x14 -> f(y',z'), x15 -> z, x16 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 8 => ('f(z,f(f(y',z'),x'))', D2, R4, P[], S{x17 -> z, x18 -> f(y',z'), x19 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 9 => ('f(y',f(f(z',x'),z))', D2, R3, P[], S{x14 -> y', x15 -> f(z',x'), x16 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 10 => ('f(z,f(z',f(x',y')))', D2, R3, P[2], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 11 => ('f(f(z',x'),f(y',z))', D2, R4, P[], S{x17 -> f(z',x'), x18 -> y', x19 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 12 => ('f(z,f(x',f(z',y')))', D2, R4, P[2], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 13 => ('f(y',f(z',f(x',z)))', D2, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 14 => ('f(z',f(y',f(x',z)))', D2, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(x',z)}), NR: 'f(z',f(y',f(x',z)))' ID: 15 => ('f(x',f(z,f(y',z')))', D2, R3, P[], S{x14 -> x', x15 -> z, x16 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 16 => ('f(z',f(f(y',x'),z))', D2, R3, P[], S{x14 -> z', x15 -> f(y',x'), x16 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 17 => ('f(z,f(y',f(x',z')))', D2, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R4, P[], S{x17 -> f(y',x'), x18 -> z', x19 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(y',f(f(z',z),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 20 => ('f(x',f(z',f(z,y')))', D3, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 21 => ('f(f(z',z),f(y',x'))', D3, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 22 => ('f(x',f(z,f(z',y')))', D3, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 23 => ('f(z',f(f(y',z),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 24 => ('f(x',f(y',f(z,z')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> z'}), NR: 'f(y',f(z,z'))' ID: 25 => ('f(f(y',z),f(z',x'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 26 => ('f(y',f(z',f(z,x')))', D3, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(z,x')}), NR: 'f(y',f(z',f(z,x')))' ID: 27 => ('f(z',f(y',f(z,x')))', D3, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(z,x')}), NR: 'f(z',f(y',f(z,x')))' ID: 28 => ('f(y',f(x',f(z',z)))', D3, R2, P[2], S{x11 -> x', x12 -> z', x13 -> z}), NR: 'f(x',f(z',z))' ID: 29 => ('f(f(z',x'),f(z,y'))', D3, R3, P[], S{x14 -> f(z',x'), x15 -> z, x16 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 30 => ('f(z,f(f(z',x'),y'))', D3, R4, P[], S{x17 -> z, x18 -> f(z',x'), x19 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 31 => ('f(z',f(f(x',y'),z))', D3, R3, P[], S{x14 -> z', x15 -> f(x',y'), x16 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 32 => ('f(f(x',y'),f(z',z))', D3, R4, P[], S{x17 -> f(x',y'), x18 -> z', x19 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 33 => ('f(z',f(x',f(y',z)))', D3, R1, P[], S{x8 -> z', x9 -> x', x10 -> f(y',z)}), NR: 'f(z',f(x',f(y',z)))' ID: 34 => ('f(y',f(z,f(z',x')))', D3, R3, P[], S{x14 -> y', x15 -> z, x16 -> f(z',x')}), NR: 'f(y',f(z,f(z',x')))' ID: 35 => ('f(x',f(f(z',y'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(z',y'), x16 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 36 => ('f(f(z',y'),f(x',z))', D3, R4, P[], S{x17 -> f(z',y'), x18 -> x', x19 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 37 => ('f(z',f(f(x',z),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 38 => ('f(y',f(x',f(z,z')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> z'}), NR: 'f(x',f(z,z'))' ID: 39 => ('f(f(x',z),f(z',y'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 40 => ('f(y',f(z,f(x',z')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> z'}), NR: 'f(z,f(x',z'))' ID: 41 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 42 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 43 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 44 => ('f(z',f(z,f(x',y')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 45 => ('f(f(y',x'),f(z,z'))', D3, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 46 => ('f(z,f(f(y',x'),z'))', D3, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 47 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 48 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 49 => ('f(z',f(z,f(y',x')))', D3, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 50 => ('f(f(z',z),f(x',y'))', D4, R3, P[], S{x14 -> f(z',z), x15 -> x', x16 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 51 => ('f(x',f(f(z',z),y'))', D4, R4, P[], S{x17 -> x', x18 -> f(z',z), x19 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 52 => ('f(z',f(f(z,y'),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 53 => ('f(f(z,y'),f(z',x'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 54 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 55 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 56 => ('f(f(y',z),f(x',z'))', D4, R3, P[], S{x14 -> f(y',z), x15 -> x', x16 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 57 => ('f(x',f(f(y',z),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(y',z), x19 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 58 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 59 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 60 => ('f(z',f(f(z,x'),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 61 => ('f(f(z,x'),f(z',y'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 62 => ('f(y',f(f(z,x'),z'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 63 => ('f(f(z,x'),f(y',z'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 64 => ('f(f(x',y'),f(z,z'))', D4, R3, P[], S{x14 -> f(x',y'), x15 -> z, x16 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 65 => ('f(z,f(f(x',y'),z'))', D4, R4, P[], S{x17 -> z, x18 -> f(x',y'), x19 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 66 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 67 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 68 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 69 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 70 => ('f(x',f(f(z,y'),z'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 71 => ('f(f(z,y'),f(x',z'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' t: f(f(x',y'),f(z',z)) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,13),(3,14),(3,15),(3,16),(4,0),(4,17),(4,18),(4,19),(5,9),(5,10),(5,11),(5,12),(6,20),(6,21),(6,22),(6,23),(7,1),(7,2),(7,24),(7,25),(8,1),(8,26),(8,27),(8,28),(9,5),(9,6),(9,7),(9,8),(10,29),(10,30),(10,31),(10,32),(11,1),(11,2),(11,3),(11,4),(12,2),(12,33),(12,34),(12,35),(13,0),(13,17),(13,18),(13,19),(14,24),(14,36),(14,37),(14,38),(15,3),(15,4),(15,23),(15,32),(16,3),(16,39),(16,40),(16,41),(17,13),(17,14),(17,15),(17,16),(18,25),(18,42),(18,43),(18,44),(19,4),(19,45),(19,46),(19,47),(20,24),(20,37),(20,48),(20,49),(21,1),(21,27),(21,50),(21,51),(22,6),(22,12),(22,40),(22,43),(23,6),(23,8),(23,52),(23,53),(24,14),(24,16),(24,54),(24,55),(25,18),(25,19),(25,56),(25,57),(26,25),(26,43),(26,58),(26,59),(27,21),(27,23),(27,60),(27,61),(28,8),(28,10),(28,37),(28,46),(29,3),(29,40),(29,62),(29,63),(30,2),(30,34),(30,64),(30,65),(31,8),(31,10),(31,37),(31,46),(32,10),(32,12),(32,66),(32,67),(33,4),(33,46),(33,68),(33,69),(34,30),(34,32),(34,70),(34,71),(35,6),(35,12),(35,40),(35,43),(36,21),(36,23),(36,60),(36,61),(37,3),(37,40),(37,62),(37,63),(38,14),(38,19),(38,27),(38,30),(39,30),(39,32),(39,70),(39,71),(40,24),(40,37),(40,48),(40,49),(41,16),(41,18),(41,21),(41,34),(42,1),(42,27),(42,50),(42,51),(43,4),(43,46),(43,68),(43,69),(44,16),(44,18),(44,21),(44,34),(45,2),(45,34),(45,64),(45,65),(46,25),(46,43),(46,58),(46,59),(47,14),(47,19),(47,27),(47,30),(48,6),(48,19),(48,30),(48,40),(49,20),(49,21),(49,22),(49,23),(50,25),(50,42),(50,43),(50,44),(51,10),(51,18),(51,21),(51,37),(52,10),(52,12),(52,66),(52,67),(53,23),(53,24),(53,25),(53,32),(54,18),(54,19),(54,56),(54,57),(55,23),(55,24),(55,25),(55,32),(56,14),(56,16),(56,54),(56,55),(57,1),(57,2),(57,24),(57,25),(58,8),(58,16),(58,34),(58,46),(59,1),(59,26),(59,27),(59,28),(60,24),(60,36),(60,37),(60,38),(61,12),(61,14),(61,27),(61,43),(62,10),(62,18),(62,21),(62,37),(63,29),(63,30),(63,31),(63,32),(64,4),(64,45),(64,46),(64,47),(65,6),(65,19),(65,30),(65,40),(66,6),(66,8),(66,52),(66,53),(67,3),(67,4),(67,23),(67,32),(68,12),(68,14),(68,27),(68,43),(69,2),(69,33),(69,34),(69,35),(70,3),(70,39),(70,40),(70,41),(71,8),(71,16),(71,34),(71,46)] ID: 0 => ('f(f(x',y'),f(z',z))', D0) ID: 1 => ('f(x',f(y',f(z',z)))', D1, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(z',z)}), NR: 'f(x',f(y',f(z',z)))' ID: 2 => ('f(y',f(x',f(z',z)))', D1, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(z',z)}), NR: 'f(y',f(x',f(z',z)))' ID: 3 => ('f(z',f(z,f(x',y')))', D1, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(x',y')}), NR: 'f(z',f(z,f(x',y')))' ID: 4 => ('f(z,f(z',f(x',y')))', D1, R4, P[], S{x17 -> z, x18 -> z', x19 -> f(x',y')}), NR: 'f(z,f(z',f(x',y')))' ID: 5 => ('f(y',f(f(z',z),x'))', D2, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 6 => ('f(x',f(z',f(z,y')))', D2, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 7 => ('f(f(z',z),f(y',x'))', D2, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 8 => ('f(x',f(z,f(z',y')))', D2, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 9 => ('f(x',f(f(z',z),y'))', D2, R3, P[], S{x14 -> x', x15 -> f(z',z), x16 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 10 => ('f(y',f(z',f(z,x')))', D2, R3, P[2], S{x14 -> z', x15 -> z, x16 -> x'}), NR: 'f(z',f(z,x'))' ID: 11 => ('f(f(z',z),f(x',y'))', D2, R4, P[], S{x17 -> f(z',z), x18 -> x', x19 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 12 => ('f(y',f(z,f(z',x')))', D2, R4, P[2], S{x17 -> z, x18 -> z', x19 -> x'}), NR: 'f(z,f(z',x'))' ID: 13 => ('f(z,f(f(x',y'),z'))', D2, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 14 => ('f(z',f(x',f(y',z)))', D2, R3, P[2], S{x14 -> x', x15 -> y', x16 -> z}), NR: 'f(x',f(y',z))' ID: 15 => ('f(f(x',y'),f(z,z'))', D2, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 16 => ('f(z',f(y',f(x',z)))', D2, R4, P[2], S{x17 -> y', x18 -> x', x19 -> z}), NR: 'f(y',f(x',z))' ID: 17 => ('f(z',f(f(x',y'),z))', D2, R3, P[], S{x14 -> z', x15 -> f(x',y'), x16 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 18 => ('f(z,f(x',f(y',z')))', D2, R3, P[2], S{x14 -> x', x15 -> y', x16 -> z'}), NR: 'f(x',f(y',z'))' ID: 19 => ('f(z,f(y',f(x',z')))', D2, R4, P[2], S{x17 -> y', x18 -> x', x19 -> z'}), NR: 'f(y',f(x',z'))' ID: 20 => ('f(z',f(f(z,y'),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 21 => ('f(x',f(z,f(y',z')))', D3, R3, P[2], S{x14 -> z, x15 -> y', x16 -> z'}), NR: 'f(z,f(y',z'))' ID: 22 => ('f(f(z,y'),f(z',x'))', D3, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 23 => ('f(x',f(y',f(z,z')))', D3, R4, P[2], S{x17 -> y', x18 -> z, x19 -> z'}), NR: 'f(y',f(z,z'))' ID: 24 => ('f(z',f(z,f(y',x')))', D3, R1, P[], S{x8 -> z', x9 -> z, x10 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 25 => ('f(z,f(z',f(y',x')))', D3, R2, P[], S{x11 -> z, x12 -> z', x13 -> f(y',x')}), NR: 'f(z,f(z',f(y',x')))' ID: 26 => ('f(z,f(f(z',y'),x'))', D3, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 27 => ('f(x',f(z',f(y',z)))', D3, R3, P[2], S{x14 -> z', x15 -> y', x16 -> z}), NR: 'f(z',f(y',z))' ID: 28 => ('f(f(z',y'),f(z,x'))', D3, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 29 => ('f(z',f(f(z,x'),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 30 => ('f(y',f(z,f(x',z')))', D3, R3, P[2], S{x14 -> z, x15 -> x', x16 -> z'}), NR: 'f(z,f(x',z'))' ID: 31 => ('f(f(z,x'),f(z',y'))', D3, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 32 => ('f(y',f(x',f(z,z')))', D3, R4, P[2], S{x17 -> x', x18 -> z, x19 -> z'}), NR: 'f(x',f(z,z'))' ID: 33 => ('f(z,f(f(z',x'),y'))', D3, R3, P[], S{x14 -> z, x15 -> f(z',x'), x16 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 34 => ('f(y',f(z',f(x',z)))', D3, R3, P[2], S{x14 -> z', x15 -> x', x16 -> z}), NR: 'f(z',f(x',z))' ID: 35 => ('f(f(z',x'),f(z,y'))', D3, R4, P[], S{x17 -> f(z',x'), x18 -> z, x19 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 36 => ('f(x',f(f(y',z),z'))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z), x16 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 37 => ('f(z',f(y',f(z,x')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> x'}), NR: 'f(y',f(z,x'))' ID: 38 => ('f(f(y',z),f(x',z'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> x', x19 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 39 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 40 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 41 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 42 => ('f(x',f(f(y',z'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 43 => ('f(z,f(y',f(z',x')))', D3, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 44 => ('f(f(y',z'),f(x',z))', D3, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 45 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 46 => ('f(z,f(x',f(z',y')))', D3, R3, P[2], S{x14 -> x', x15 -> z', x16 -> y'}), NR: 'f(x',f(z',y'))' ID: 47 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 48 => ('f(f(z,y'),f(x',z'))', D4, R3, P[], S{x14 -> f(z,y'), x15 -> x', x16 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 49 => ('f(x',f(f(z,y'),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(z,y'), x19 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 50 => ('f(z,f(f(y',z'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',z'), x16 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 51 => ('f(f(y',z'),f(z,x'))', D4, R4, P[], S{x17 -> f(y',z'), x18 -> z, x19 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 52 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 53 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 54 => ('f(z,f(f(y',x'),z'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',x'), x16 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 55 => ('f(f(y',x'),f(z,z'))', D4, R4, P[], S{x17 -> f(y',x'), x18 -> z, x19 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 56 => ('f(z',f(f(y',x'),z))', D4, R3, P[], S{x14 -> z', x15 -> f(y',x'), x16 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 57 => ('f(f(y',x'),f(z',z))', D4, R4, P[], S{x17 -> f(y',x'), x18 -> z', x19 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 58 => ('f(f(z',y'),f(x',z))', D4, R3, P[], S{x14 -> f(z',y'), x15 -> x', x16 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 59 => ('f(x',f(f(z',y'),z))', D4, R4, P[], S{x17 -> x', x18 -> f(z',y'), x19 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 60 => ('f(z',f(f(y',z),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 61 => ('f(f(y',z),f(z',x'))', D4, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 62 => ('f(f(z,x'),f(y',z'))', D4, R3, P[], S{x14 -> f(z,x'), x15 -> y', x16 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 63 => ('f(y',f(f(z,x'),z'))', D4, R4, P[], S{x17 -> y', x18 -> f(z,x'), x19 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 64 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 65 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 66 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 67 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 68 => ('f(f(z',x'),f(y',z))', D4, R3, P[], S{x14 -> f(z',x'), x15 -> y', x16 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 69 => ('f(y',f(f(z',x'),z))', D4, R4, P[], S{x17 -> y', x18 -> f(z',x'), x19 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 70 => ('f(z',f(f(x',z),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 71 => ('f(f(x',z),f(z',y'))', D4, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' SNodesPath1: f(z,f(x',f(y',z'))) TNodesPath1: f(f(x',y'),f(z',z)) -> f(x',f(y',f(z',z))) -> f(y',f(f(z',z),x')) -> f(x',f(f(z',z),y')) -> f(x',f(z',f(z,y'))) -> f(z',f(f(z,y'),x')) -> f(z',f(z,f(y',x'))) -> f(z',f(x',f(y',z))) -> f(x',f(f(y',z),z')) -> f(x',f(z,f(y',z'))) -> f(x',f(z',f(y',z))) -> f(x',f(y',f(z,z'))) -> f(x',f(z,f(z',y'))) -> f(z,f(f(z',y'),x')) -> f(z,f(z',f(y',x'))) -> f(z,f(x',f(y',z'))) SNodesPath2: TNodesPath2: f(f(x',y'),f(z',z)) f(z,f(x',f(y',z'))) ->= f(z,f(x',f(y',z'))) *<- f(f(x',y'),f(z',z)) f(f(x',y'),f(z',z)) ->= f(f(x',y'),f(z',z)) *<- f(z,f(x',f(y',z'))) "Strongly closed critical pair" The problem is confluent. Problem 1.9: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Not overlay, Proper, NW0, N18 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(f(x',f(y',z')),z) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,13),(3,14),(3,15),(3,16),(4,0),(4,17),(4,18),(4,19),(5,20),(5,21),(5,22),(5,23),(6,11),(6,24),(6,25),(6,26),(7,11),(7,12),(7,27),(7,28),(8,1),(8,2),(8,29),(8,30),(9,31),(9,32),(9,33),(9,34),(10,35),(10,36),(10,37),(10,38),(11,5),(11,6),(11,7),(11,8),(12,1),(12,2),(12,29),(12,30),(13,9),(13,39),(13,40),(13,41),(14,6),(14,29),(14,42),(14,43),(15,0),(15,19),(15,44),(15,45),(16,3),(16,4),(16,46),(16,47),(17,10),(17,42),(17,48),(17,49),(18,5),(18,30),(18,39),(18,50),(19,15),(19,16),(19,51),(19,52),(20,27),(20,43),(20,53),(20,54),(21,11),(21,25),(21,55),(21,56),(22,5),(22,30),(22,39),(22,50),(23,5),(23,6),(23,57),(23,58),(24,28),(24,50),(24,59),(24,60),(25,21),(25,23),(25,61),(25,62),(26,6),(26,29),(26,42),(26,43),(27,32),(27,34),(27,63),(27,64),(28,36),(28,38),(28,65),(28,66),(29,13),(29,14),(29,67),(29,68),(30,12),(30,17),(30,18),(30,69),(31,35),(31,36),(31,37),(31,38),(32,27),(32,43),(32,70),(32,71),(33,9),(33,10),(33,23),(33,68),(34,9),(34,39),(34,72),(34,73),(35,31),(35,32),(35,33),(35,34),(36,28),(36,50),(36,74),(36,75),(37,9),(37,10),(37,11),(37,12),(38,10),(38,42),(38,76),(38,77),(39,27),(39,43),(39,53),(39,54),(40,21),(40,29),(40,36),(40,43),(41,13),(41,14),(41,67),(41,68),(42,28),(42,50),(42,59),(42,60),(43,9),(43,39),(43,40),(43,41),(44,10),(44,42),(44,76),(44,77),(45,5),(45,38),(45,39),(45,67),(46,5),(46,6),(46,57),(46,58),(47,9),(47,10),(47,23),(47,68),(48,25),(48,30),(48,32),(48,50),(49,12),(49,17),(49,18),(49,69),(50,10),(50,42),(50,48),(50,49),(51,9),(51,39),(51,72),(51,73),(52,6),(52,34),(52,42),(52,69),(53,5),(53,38),(53,39),(53,67),(54,20),(54,21),(54,22),(54,23),(55,28),(55,50),(55,74),(55,75),(56,21),(56,29),(56,36),(56,43),(57,29),(57,30),(57,46),(57,47),(58,23),(58,27),(58,28),(58,68),(59,6),(59,34),(59,42),(59,69),(60,11),(60,24),(60,25),(60,26),(61,27),(61,43),(61,70),(61,71),(62,25),(62,30),(62,32),(62,50),(63,36),(63,38),(63,65),(63,66),(64,23),(64,27),(64,28),(64,68),(65,32),(65,34),(65,63),(65,64),(66,11),(66,12),(66,27),(66,28),(67,12),(67,44),(67,45),(67,69),(68,29),(68,30),(68,46),(68,47),(69,51),(69,52),(69,67),(69,68),(70,21),(70,23),(70,61),(70,62),(71,25),(71,32),(71,38),(71,67),(72,51),(72,52),(72,67),(72,68),(73,21),(73,34),(73,36),(73,69),(74,11),(74,25),(74,55),(74,56),(75,21),(75,34),(75,36),(75,69),(76,12),(76,44),(76,45),(76,69),(77,25),(77,32),(77,38),(77,67)] ID: 0 => ('f(f(x',f(y',z')),z)', D0) ID: 1 => ('f(x',f(f(y',z'),z))', D1, R1, P[], S{x8 -> x', x9 -> f(y',z'), x10 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 2 => ('f(f(y',z'),f(x',z))', D1, R2, P[], S{x11 -> f(y',z'), x12 -> x', x13 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 3 => ('f(f(y',f(z',x')),z)', D1, R3, P[1], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 4 => ('f(f(z',f(y',x')),z)', D1, R4, P[1], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 5 => ('f(x',f(y',f(z',z)))', D2, R1, P[2], S{x8 -> y', x9 -> z', x10 -> z}), NR: 'f(y',f(z',z))' ID: 6 => ('f(x',f(z',f(y',z)))', D2, R2, P[2], S{x11 -> z', x12 -> y', x13 -> z}), NR: 'f(z',f(y',z))' ID: 7 => ('f(f(y',z'),f(z,x'))', D2, R3, P[], S{x14 -> f(y',z'), x15 -> z, x16 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 8 => ('f(z,f(f(y',z'),x'))', D2, R4, P[], S{x17 -> z, x18 -> f(y',z'), x19 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 9 => ('f(y',f(z',f(x',z)))', D2, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 10 => ('f(z',f(y',f(x',z)))', D2, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(x',z)}), NR: 'f(z',f(y',f(x',z)))' ID: 11 => ('f(x',f(z,f(y',z')))', D2, R3, P[], S{x14 -> x', x15 -> z, x16 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 12 => ('f(z,f(x',f(y',z')))', D2, R4, P[], S{x17 -> z, x18 -> x', x19 -> f(y',z')}), NR: 'f(z,f(x',f(y',z')))' ID: 13 => ('f(y',f(f(z',x'),z))', D2, R1, P[], S{x8 -> y', x9 -> f(z',x'), x10 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 14 => ('f(f(z',x'),f(y',z))', D2, R2, P[], S{x11 -> f(z',x'), x12 -> y', x13 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 15 => ('f(f(z',f(x',y')),z)', D2, R3, P[1], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 16 => ('f(f(x',f(z',y')),z)', D2, R4, P[1], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 17 => ('f(z',f(f(y',x'),z))', D2, R1, P[], S{x8 -> z', x9 -> f(y',x'), x10 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R2, P[], S{x11 -> f(y',x'), x12 -> z', x13 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(f(y',f(x',z')),z)', D2, R3, P[1], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 20 => ('f(y',f(f(z',z),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 21 => ('f(x',f(z',f(z,y')))', D3, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 22 => ('f(f(z',z),f(y',x'))', D3, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 23 => ('f(x',f(z,f(z',y')))', D3, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 24 => ('f(z',f(f(y',z),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 25 => ('f(x',f(y',f(z,z')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> z'}), NR: 'f(y',f(z,z'))' ID: 26 => ('f(f(y',z),f(z',x'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 27 => ('f(y',f(z',f(z,x')))', D3, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(z,x')}), NR: 'f(y',f(z',f(z,x')))' ID: 28 => ('f(z',f(y',f(z,x')))', D3, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(z,x')}), NR: 'f(z',f(y',f(z,x')))' ID: 29 => ('f(z,f(y',f(z',x')))', D3, R1, P[2], S{x8 -> y', x9 -> z', x10 -> x'}), NR: 'f(y',f(z',x'))' ID: 30 => ('f(z,f(z',f(y',x')))', D3, R2, P[2], S{x11 -> z', x12 -> y', x13 -> x'}), NR: 'f(z',f(y',x'))' ID: 31 => ('f(z',f(f(x',z),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 32 => ('f(y',f(x',f(z,z')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> z'}), NR: 'f(x',f(z,z'))' ID: 33 => ('f(f(x',z),f(z',y'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 34 => ('f(y',f(z,f(x',z')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> z'}), NR: 'f(z,f(x',z'))' ID: 35 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 36 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 37 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 38 => ('f(z',f(z,f(x',y')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 39 => ('f(y',f(x',f(z',z)))', D3, R2, P[2], S{x11 -> x', x12 -> z', x13 -> z}), NR: 'f(x',f(z',z))' ID: 40 => ('f(f(z',x'),f(z,y'))', D3, R3, P[], S{x14 -> f(z',x'), x15 -> z, x16 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 41 => ('f(z,f(f(z',x'),y'))', D3, R4, P[], S{x17 -> z, x18 -> f(z',x'), x19 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 42 => ('f(z',f(x',f(y',z)))', D3, R1, P[], S{x8 -> z', x9 -> x', x10 -> f(y',z)}), NR: 'f(z',f(x',f(y',z)))' ID: 43 => ('f(y',f(z,f(z',x')))', D3, R3, P[], S{x14 -> y', x15 -> z, x16 -> f(z',x')}), NR: 'f(y',f(z,f(z',x')))' ID: 44 => ('f(z',f(f(x',y'),z))', D3, R1, P[], S{x8 -> z', x9 -> f(x',y'), x10 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 45 => ('f(f(x',y'),f(z',z))', D3, R2, P[], S{x11 -> f(x',y'), x12 -> z', x13 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 46 => ('f(x',f(f(z',y'),z))', D3, R1, P[], S{x8 -> x', x9 -> f(z',y'), x10 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 47 => ('f(f(z',y'),f(x',z))', D3, R2, P[], S{x11 -> f(z',y'), x12 -> x', x13 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 48 => ('f(f(y',x'),f(z,z'))', D3, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 49 => ('f(z,f(f(y',x'),z'))', D3, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 50 => ('f(z',f(z,f(y',x')))', D3, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 51 => ('f(y',f(f(x',z'),z))', D3, R1, P[], S{x8 -> y', x9 -> f(x',z'), x10 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 52 => ('f(f(x',z'),f(y',z))', D3, R2, P[], S{x11 -> f(x',z'), x12 -> y', x13 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 53 => ('f(f(z',z),f(x',y'))', D4, R3, P[], S{x14 -> f(z',z), x15 -> x', x16 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 54 => ('f(x',f(f(z',z),y'))', D4, R4, P[], S{x17 -> x', x18 -> f(z',z), x19 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 55 => ('f(z',f(f(z,y'),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 56 => ('f(f(z,y'),f(z',x'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 57 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 58 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 59 => ('f(f(y',z),f(x',z'))', D4, R3, P[], S{x14 -> f(y',z), x15 -> x', x16 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 60 => ('f(x',f(f(y',z),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(y',z), x19 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 61 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 62 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 63 => ('f(z',f(f(z,x'),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 64 => ('f(f(z,x'),f(z',y'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 65 => ('f(y',f(f(z,x'),z'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 66 => ('f(f(z,x'),f(y',z'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 67 => ('f(z,f(z',f(x',y')))', D4, R3, P[2], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 68 => ('f(z,f(x',f(z',y')))', D4, R4, P[2], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 69 => ('f(z,f(y',f(x',z')))', D4, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 70 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 71 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 72 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 73 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 74 => ('f(x',f(f(z,y'),z'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 75 => ('f(f(z,y'),f(x',z'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 76 => ('f(z,f(f(x',y'),z'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 77 => ('f(f(x',y'),f(z,z'))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' t: f(z',f(f(y',x'),z)) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,12),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,13),(5,19),(5,20),(5,21),(6,10),(6,12),(6,22),(6,23),(7,1),(7,17),(7,24),(7,25),(8,1),(8,2),(8,26),(8,27),(9,14),(9,24),(9,28),(9,29),(10,6),(10,8),(10,30),(10,31),(11,2),(11,16),(11,19),(11,32),(12,1),(12,2),(12,3),(12,4),(13,33),(13,34),(13,35),(13,36),(14,37),(14,38),(14,39),(14,40),(15,0),(15,16),(15,17),(15,18),(16,41),(16,42),(16,43),(16,44),(17,15),(17,45),(17,46),(17,47),(18,12),(18,15),(18,48),(18,49),(19,25),(19,48),(19,50),(19,51),(20,1),(20,25),(20,38),(20,42),(21,5),(21,6),(21,7),(21,8),(22,14),(22,24),(22,52),(22,53),(23,6),(23,16),(23,19),(23,40),(24,32),(24,49),(24,54),(24,55),(25,13),(25,19),(25,20),(25,21),(26,16),(26,17),(26,56),(26,57),(27,8),(27,13),(27,14),(27,44),(28,2),(28,32),(28,34),(28,46),(29,9),(29,10),(29,11),(29,12),(30,13),(30,19),(30,58),(30,59),(31,10),(31,17),(31,24),(31,36),(32,14),(32,24),(32,28),(32,29),(33,37),(33,38),(33,39),(33,40),(34,25),(34,48),(34,60),(34,61),(35,8),(35,13),(35,14),(35,44),(36,13),(36,19),(36,58),(36,59),(37,33),(37,34),(37,35),(37,36),(38,32),(38,49),(38,62),(38,63),(39,12),(39,13),(39,14),(39,15),(40,14),(40,24),(40,52),(40,53),(41,25),(41,48),(41,50),(41,51),(42,15),(42,46),(42,64),(42,65),(43,2),(43,16),(43,19),(43,32),(44,16),(44,17),(44,56),(44,57),(45,32),(45,49),(45,54),(45,55),(46,42),(46,44),(46,66),(46,67),(47,1),(47,17),(47,24),(47,25),(48,34),(48,36),(48,68),(48,69),(49,38),(49,40),(49,70),(49,71),(50,41),(50,42),(50,43),(50,44),(51,6),(51,16),(51,19),(51,40),(52,6),(52,34),(52,40),(52,46),(53,10),(53,12),(53,22),(53,23),(54,15),(54,45),(54,46),(54,47),(55,10),(55,17),(55,24),(55,36),(56,8),(56,44),(56,48),(56,49),(57,1),(57,2),(57,26),(57,27),(58,10),(58,36),(58,38),(58,42),(59,6),(59,8),(59,30),(59,31),(60,42),(60,44),(60,66),(60,67),(61,6),(61,34),(61,40),(61,46),(62,15),(62,46),(62,64),(62,65),(63,10),(63,36),(63,38),(63,42),(64,32),(64,49),(64,62),(64,63),(65,1),(65,25),(65,38),(65,42),(66,25),(66,48),(66,60),(66,61),(67,2),(67,32),(67,34),(67,46),(68,38),(68,40),(68,70),(68,71),(69,8),(69,44),(69,48),(69,49),(70,34),(70,36),(70,68),(70,69),(71,12),(71,15),(71,48),(71,49)] ID: 0 => ('f(z',f(f(y',x'),z))', D0) ID: 1 => ('f(z',f(y',f(x',z)))', D1, R1, P[2], S{x8 -> y', x9 -> x', x10 -> z}), NR: 'f(y',f(x',z))' ID: 2 => ('f(z',f(x',f(y',z)))', D1, R2, P[2], S{x11 -> x', x12 -> y', x13 -> z}), NR: 'f(x',f(y',z))' ID: 3 => ('f(f(y',x'),f(z,z'))', D1, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 4 => ('f(z,f(f(y',x'),z'))', D1, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 5 => ('f(y',f(f(x',z),z'))', D2, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 6 => ('f(z',f(x',f(z,y')))', D2, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 7 => ('f(f(x',z),f(y',z'))', D2, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 8 => ('f(z',f(z,f(x',y')))', D2, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 9 => ('f(x',f(f(y',z),z'))', D2, R3, P[], S{x14 -> x', x15 -> f(y',z), x16 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 10 => ('f(z',f(y',f(z,x')))', D2, R3, P[2], S{x14 -> y', x15 -> z, x16 -> x'}), NR: 'f(y',f(z,x'))' ID: 11 => ('f(f(y',z),f(x',z'))', D2, R4, P[], S{x17 -> f(y',z), x18 -> x', x19 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 12 => ('f(z',f(z,f(y',x')))', D2, R4, P[2], S{x17 -> z, x18 -> y', x19 -> x'}), NR: 'f(z,f(y',x'))' ID: 13 => ('f(y',f(x',f(z,z')))', D2, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(z,z')}), NR: 'f(y',f(x',f(z,z')))' ID: 14 => ('f(x',f(y',f(z,z')))', D2, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(z,z')}), NR: 'f(x',f(y',f(z,z')))' ID: 15 => ('f(z,f(z',f(y',x')))', D2, R3, P[], S{x14 -> z, x15 -> z', x16 -> f(y',x')}), NR: 'f(z,f(z',f(y',x')))' ID: 16 => ('f(z,f(y',f(x',z')))', D2, R1, P[2], S{x8 -> y', x9 -> x', x10 -> z'}), NR: 'f(y',f(x',z'))' ID: 17 => ('f(z,f(x',f(y',z')))', D2, R2, P[2], S{x11 -> x', x12 -> y', x13 -> z'}), NR: 'f(x',f(y',z'))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R3, P[], S{x14 -> f(y',x'), x15 -> z', x16 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(y',f(z,f(x',z')))', D3, R2, P[2], S{x11 -> z, x12 -> x', x13 -> z'}), NR: 'f(z,f(x',z'))' ID: 20 => ('f(f(x',z),f(z',y'))', D3, R3, P[], S{x14 -> f(x',z), x15 -> z', x16 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 21 => ('f(z',f(f(x',z),y'))', D3, R4, P[], S{x17 -> z', x18 -> f(x',z), x19 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 22 => ('f(x',f(f(z,y'),z'))', D3, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 23 => ('f(f(z,y'),f(x',z'))', D3, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 24 => ('f(x',f(z,f(y',z')))', D3, R1, P[], S{x8 -> x', x9 -> z, x10 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 25 => ('f(y',f(z',f(x',z)))', D3, R3, P[], S{x14 -> y', x15 -> z', x16 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 26 => ('f(z,f(f(x',y'),z'))', D3, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 27 => ('f(f(x',y'),f(z,z'))', D3, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 28 => ('f(f(y',z),f(z',x'))', D3, R3, P[], S{x14 -> f(y',z), x15 -> z', x16 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 29 => ('f(z',f(f(y',z),x'))', D3, R4, P[], S{x17 -> z', x18 -> f(y',z), x19 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 30 => ('f(y',f(f(z,x'),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 31 => ('f(f(z,x'),f(y',z'))', D3, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 32 => ('f(x',f(z',f(y',z)))', D3, R3, P[], S{x14 -> x', x15 -> z', x16 -> f(y',z)}), NR: 'f(x',f(z',f(y',z)))' ID: 33 => ('f(x',f(f(z,z'),y'))', D3, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 34 => ('f(y',f(z,f(z',x')))', D3, R3, P[2], S{x14 -> z, x15 -> z', x16 -> x'}), NR: 'f(z,f(z',x'))' ID: 35 => ('f(f(z,z'),f(x',y'))', D3, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 36 => ('f(y',f(z',f(z,x')))', D3, R4, P[2], S{x17 -> z', x18 -> z, x19 -> x'}), NR: 'f(z',f(z,x'))' ID: 37 => ('f(y',f(f(z,z'),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 38 => ('f(x',f(z,f(z',y')))', D3, R3, P[2], S{x14 -> z, x15 -> z', x16 -> y'}), NR: 'f(z,f(z',y'))' ID: 39 => ('f(f(z,z'),f(y',x'))', D3, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 40 => ('f(x',f(z',f(z,y')))', D3, R4, P[2], S{x17 -> z', x18 -> z, x19 -> y'}), NR: 'f(z',f(z,y'))' ID: 41 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 42 => ('f(z,f(x',f(z',y')))', D3, R3, P[2], S{x14 -> x', x15 -> z', x16 -> y'}), NR: 'f(x',f(z',y'))' ID: 43 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 44 => ('f(z,f(z',f(x',y')))', D3, R4, P[2], S{x17 -> z', x18 -> x', x19 -> y'}), NR: 'f(z',f(x',y'))' ID: 45 => ('f(x',f(f(y',z'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 46 => ('f(z,f(y',f(z',x')))', D3, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 47 => ('f(f(y',z'),f(x',z))', D3, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 48 => ('f(y',f(x',f(z',z)))', D3, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(z',z)}), NR: 'f(y',f(x',f(z',z)))' ID: 49 => ('f(x',f(y',f(z',z)))', D3, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(z',z)}), NR: 'f(x',f(y',f(z',z)))' ID: 50 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 51 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 52 => ('f(f(z,y'),f(z',x'))', D4, R3, P[], S{x14 -> f(z,y'), x15 -> z', x16 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 53 => ('f(z',f(f(z,y'),x'))', D4, R4, P[], S{x17 -> z', x18 -> f(z,y'), x19 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 54 => ('f(z,f(f(y',z'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',z'), x16 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 55 => ('f(f(y',z'),f(z,x'))', D4, R4, P[], S{x17 -> f(y',z'), x18 -> z, x19 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 56 => ('f(f(x',y'),f(z',z))', D4, R3, P[], S{x14 -> f(x',y'), x15 -> z', x16 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 57 => ('f(z',f(f(x',y'),z))', D4, R4, P[], S{x17 -> z', x18 -> f(x',y'), x19 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 58 => ('f(f(z,x'),f(z',y'))', D4, R3, P[], S{x14 -> f(z,x'), x15 -> z', x16 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 59 => ('f(z',f(f(z,x'),y'))', D4, R4, P[], S{x17 -> z', x18 -> f(z,x'), x19 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 60 => ('f(z,f(f(z',x'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',x'), x16 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 61 => ('f(f(z',x'),f(z,y'))', D4, R4, P[], S{x17 -> f(z',x'), x18 -> z, x19 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 62 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 63 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 64 => ('f(x',f(f(z',y'),z))', D4, R3, P[], S{x14 -> x', x15 -> f(z',y'), x16 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 65 => ('f(f(z',y'),f(x',z))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> x', x19 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 66 => ('f(y',f(f(z',x'),z))', D4, R3, P[], S{x14 -> y', x15 -> f(z',x'), x16 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 67 => ('f(f(z',x'),f(y',z))', D4, R4, P[], S{x17 -> f(z',x'), x18 -> y', x19 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 68 => ('f(x',f(f(z',z),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z',z), x16 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 69 => ('f(f(z',z),f(x',y'))', D4, R4, P[], S{x17 -> f(z',z), x18 -> x', x19 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 70 => ('f(y',f(f(z',z),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 71 => ('f(f(z',z),f(y',x'))', D4, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' SNodesPath1: f(f(x',f(y',z')),z) -> f(x',f(f(y',z'),z)) TNodesPath1: SNodesPath2: TNodesPath2: f(z',f(f(y',x'),z)) f(f(x',f(y',z')),z) ->= f(x',f(f(y',z'),z)) *<- f(z',f(f(y',x'),z)) f(z',f(f(y',x'),z)) ->= f(z',f(f(y',x'),z)) *<- f(f(x',f(y',z')),z) "Strongly closed critical pair" The problem is confluent. Problem 1.10: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Not overlay, Proper, NW0, N19 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(z,f(x',f(y',z'))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(z,f(x',f(y',z')))', D0) ID: 1 => ('f(x',f(f(y',z'),z))', D1, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 2 => ('f(z,f(y',f(z',x')))', D1, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 3 => ('f(f(y',z'),f(x',z))', D1, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 4 => ('f(z,f(z',f(y',x')))', D1, R4, P[2], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 5 => ('f(x',f(y',f(z',z)))', D2, R1, P[2], S{x8 -> y', x9 -> z', x10 -> z}), NR: 'f(y',f(z',z))' ID: 6 => ('f(x',f(z',f(y',z)))', D2, R2, P[2], S{x11 -> z', x12 -> y', x13 -> z}), NR: 'f(z',f(y',z))' ID: 7 => ('f(f(y',z'),f(z,x'))', D2, R3, P[], S{x14 -> f(y',z'), x15 -> z, x16 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 8 => ('f(z,f(f(y',z'),x'))', D2, R4, P[], S{x17 -> z, x18 -> f(y',z'), x19 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 9 => ('f(y',f(f(z',x'),z))', D2, R3, P[], S{x14 -> y', x15 -> f(z',x'), x16 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 10 => ('f(z,f(z',f(x',y')))', D2, R3, P[2], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 11 => ('f(f(z',x'),f(y',z))', D2, R4, P[], S{x17 -> f(z',x'), x18 -> y', x19 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 12 => ('f(z,f(x',f(z',y')))', D2, R4, P[2], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 13 => ('f(y',f(z',f(x',z)))', D2, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 14 => ('f(z',f(y',f(x',z)))', D2, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(x',z)}), NR: 'f(z',f(y',f(x',z)))' ID: 15 => ('f(x',f(z,f(y',z')))', D2, R3, P[], S{x14 -> x', x15 -> z, x16 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 16 => ('f(z',f(f(y',x'),z))', D2, R3, P[], S{x14 -> z', x15 -> f(y',x'), x16 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 17 => ('f(z,f(y',f(x',z')))', D2, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R4, P[], S{x17 -> f(y',x'), x18 -> z', x19 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(y',f(f(z',z),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 20 => ('f(x',f(z',f(z,y')))', D3, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 21 => ('f(f(z',z),f(y',x'))', D3, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 22 => ('f(x',f(z,f(z',y')))', D3, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 23 => ('f(z',f(f(y',z),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 24 => ('f(x',f(y',f(z,z')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> z'}), NR: 'f(y',f(z,z'))' ID: 25 => ('f(f(y',z),f(z',x'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 26 => ('f(y',f(z',f(z,x')))', D3, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(z,x')}), NR: 'f(y',f(z',f(z,x')))' ID: 27 => ('f(z',f(y',f(z,x')))', D3, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(z,x')}), NR: 'f(z',f(y',f(z,x')))' ID: 28 => ('f(y',f(x',f(z',z)))', D3, R2, P[2], S{x11 -> x', x12 -> z', x13 -> z}), NR: 'f(x',f(z',z))' ID: 29 => ('f(f(z',x'),f(z,y'))', D3, R3, P[], S{x14 -> f(z',x'), x15 -> z, x16 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 30 => ('f(z,f(f(z',x'),y'))', D3, R4, P[], S{x17 -> z, x18 -> f(z',x'), x19 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 31 => ('f(z',f(f(x',y'),z))', D3, R3, P[], S{x14 -> z', x15 -> f(x',y'), x16 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 32 => ('f(f(x',y'),f(z',z))', D3, R4, P[], S{x17 -> f(x',y'), x18 -> z', x19 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 33 => ('f(z',f(x',f(y',z)))', D3, R1, P[], S{x8 -> z', x9 -> x', x10 -> f(y',z)}), NR: 'f(z',f(x',f(y',z)))' ID: 34 => ('f(y',f(z,f(z',x')))', D3, R3, P[], S{x14 -> y', x15 -> z, x16 -> f(z',x')}), NR: 'f(y',f(z,f(z',x')))' ID: 35 => ('f(x',f(f(z',y'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(z',y'), x16 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 36 => ('f(f(z',y'),f(x',z))', D3, R4, P[], S{x17 -> f(z',y'), x18 -> x', x19 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 37 => ('f(z',f(f(x',z),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 38 => ('f(y',f(x',f(z,z')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> z'}), NR: 'f(x',f(z,z'))' ID: 39 => ('f(f(x',z),f(z',y'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 40 => ('f(y',f(z,f(x',z')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> z'}), NR: 'f(z,f(x',z'))' ID: 41 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 42 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 43 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 44 => ('f(z',f(z,f(x',y')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 45 => ('f(f(y',x'),f(z,z'))', D3, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 46 => ('f(z,f(f(y',x'),z'))', D3, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 47 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 48 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 49 => ('f(z',f(z,f(y',x')))', D3, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 50 => ('f(f(z',z),f(x',y'))', D4, R3, P[], S{x14 -> f(z',z), x15 -> x', x16 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 51 => ('f(x',f(f(z',z),y'))', D4, R4, P[], S{x17 -> x', x18 -> f(z',z), x19 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 52 => ('f(z',f(f(z,y'),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 53 => ('f(f(z,y'),f(z',x'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 54 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 55 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 56 => ('f(f(y',z),f(x',z'))', D4, R3, P[], S{x14 -> f(y',z), x15 -> x', x16 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 57 => ('f(x',f(f(y',z),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(y',z), x19 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 58 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 59 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 60 => ('f(z',f(f(z,x'),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 61 => ('f(f(z,x'),f(z',y'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 62 => ('f(y',f(f(z,x'),z'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 63 => ('f(f(z,x'),f(y',z'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 64 => ('f(f(x',y'),f(z,z'))', D4, R3, P[], S{x14 -> f(x',y'), x15 -> z, x16 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 65 => ('f(z,f(f(x',y'),z'))', D4, R4, P[], S{x17 -> z, x18 -> f(x',y'), x19 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 66 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 67 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 68 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 69 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 70 => ('f(x',f(f(z,y'),z'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 71 => ('f(f(z,y'),f(x',z'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' t: f(z',f(f(y',x'),z)) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,12),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,13),(5,19),(5,20),(5,21),(6,10),(6,12),(6,22),(6,23),(7,1),(7,17),(7,24),(7,25),(8,1),(8,2),(8,26),(8,27),(9,14),(9,24),(9,28),(9,29),(10,6),(10,8),(10,30),(10,31),(11,2),(11,16),(11,19),(11,32),(12,1),(12,2),(12,3),(12,4),(13,33),(13,34),(13,35),(13,36),(14,37),(14,38),(14,39),(14,40),(15,0),(15,16),(15,17),(15,18),(16,41),(16,42),(16,43),(16,44),(17,15),(17,45),(17,46),(17,47),(18,12),(18,15),(18,48),(18,49),(19,25),(19,48),(19,50),(19,51),(20,1),(20,25),(20,38),(20,42),(21,5),(21,6),(21,7),(21,8),(22,14),(22,24),(22,52),(22,53),(23,6),(23,16),(23,19),(23,40),(24,32),(24,49),(24,54),(24,55),(25,13),(25,19),(25,20),(25,21),(26,16),(26,17),(26,56),(26,57),(27,8),(27,13),(27,14),(27,44),(28,2),(28,32),(28,34),(28,46),(29,9),(29,10),(29,11),(29,12),(30,13),(30,19),(30,58),(30,59),(31,10),(31,17),(31,24),(31,36),(32,14),(32,24),(32,28),(32,29),(33,37),(33,38),(33,39),(33,40),(34,25),(34,48),(34,60),(34,61),(35,8),(35,13),(35,14),(35,44),(36,13),(36,19),(36,58),(36,59),(37,33),(37,34),(37,35),(37,36),(38,32),(38,49),(38,62),(38,63),(39,12),(39,13),(39,14),(39,15),(40,14),(40,24),(40,52),(40,53),(41,25),(41,48),(41,50),(41,51),(42,15),(42,46),(42,64),(42,65),(43,2),(43,16),(43,19),(43,32),(44,16),(44,17),(44,56),(44,57),(45,32),(45,49),(45,54),(45,55),(46,42),(46,44),(46,66),(46,67),(47,1),(47,17),(47,24),(47,25),(48,34),(48,36),(48,68),(48,69),(49,38),(49,40),(49,70),(49,71),(50,41),(50,42),(50,43),(50,44),(51,6),(51,16),(51,19),(51,40),(52,6),(52,34),(52,40),(52,46),(53,10),(53,12),(53,22),(53,23),(54,15),(54,45),(54,46),(54,47),(55,10),(55,17),(55,24),(55,36),(56,8),(56,44),(56,48),(56,49),(57,1),(57,2),(57,26),(57,27),(58,10),(58,36),(58,38),(58,42),(59,6),(59,8),(59,30),(59,31),(60,42),(60,44),(60,66),(60,67),(61,6),(61,34),(61,40),(61,46),(62,15),(62,46),(62,64),(62,65),(63,10),(63,36),(63,38),(63,42),(64,32),(64,49),(64,62),(64,63),(65,1),(65,25),(65,38),(65,42),(66,25),(66,48),(66,60),(66,61),(67,2),(67,32),(67,34),(67,46),(68,38),(68,40),(68,70),(68,71),(69,8),(69,44),(69,48),(69,49),(70,34),(70,36),(70,68),(70,69),(71,12),(71,15),(71,48),(71,49)] ID: 0 => ('f(z',f(f(y',x'),z))', D0) ID: 1 => ('f(z',f(y',f(x',z)))', D1, R1, P[2], S{x8 -> y', x9 -> x', x10 -> z}), NR: 'f(y',f(x',z))' ID: 2 => ('f(z',f(x',f(y',z)))', D1, R2, P[2], S{x11 -> x', x12 -> y', x13 -> z}), NR: 'f(x',f(y',z))' ID: 3 => ('f(f(y',x'),f(z,z'))', D1, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 4 => ('f(z,f(f(y',x'),z'))', D1, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 5 => ('f(y',f(f(x',z),z'))', D2, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 6 => ('f(z',f(x',f(z,y')))', D2, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 7 => ('f(f(x',z),f(y',z'))', D2, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 8 => ('f(z',f(z,f(x',y')))', D2, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 9 => ('f(x',f(f(y',z),z'))', D2, R3, P[], S{x14 -> x', x15 -> f(y',z), x16 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 10 => ('f(z',f(y',f(z,x')))', D2, R3, P[2], S{x14 -> y', x15 -> z, x16 -> x'}), NR: 'f(y',f(z,x'))' ID: 11 => ('f(f(y',z),f(x',z'))', D2, R4, P[], S{x17 -> f(y',z), x18 -> x', x19 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 12 => ('f(z',f(z,f(y',x')))', D2, R4, P[2], S{x17 -> z, x18 -> y', x19 -> x'}), NR: 'f(z,f(y',x'))' ID: 13 => ('f(y',f(x',f(z,z')))', D2, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(z,z')}), NR: 'f(y',f(x',f(z,z')))' ID: 14 => ('f(x',f(y',f(z,z')))', D2, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(z,z')}), NR: 'f(x',f(y',f(z,z')))' ID: 15 => ('f(z,f(z',f(y',x')))', D2, R3, P[], S{x14 -> z, x15 -> z', x16 -> f(y',x')}), NR: 'f(z,f(z',f(y',x')))' ID: 16 => ('f(z,f(y',f(x',z')))', D2, R1, P[2], S{x8 -> y', x9 -> x', x10 -> z'}), NR: 'f(y',f(x',z'))' ID: 17 => ('f(z,f(x',f(y',z')))', D2, R2, P[2], S{x11 -> x', x12 -> y', x13 -> z'}), NR: 'f(x',f(y',z'))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R3, P[], S{x14 -> f(y',x'), x15 -> z', x16 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(y',f(z,f(x',z')))', D3, R2, P[2], S{x11 -> z, x12 -> x', x13 -> z'}), NR: 'f(z,f(x',z'))' ID: 20 => ('f(f(x',z),f(z',y'))', D3, R3, P[], S{x14 -> f(x',z), x15 -> z', x16 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 21 => ('f(z',f(f(x',z),y'))', D3, R4, P[], S{x17 -> z', x18 -> f(x',z), x19 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 22 => ('f(x',f(f(z,y'),z'))', D3, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 23 => ('f(f(z,y'),f(x',z'))', D3, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 24 => ('f(x',f(z,f(y',z')))', D3, R1, P[], S{x8 -> x', x9 -> z, x10 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 25 => ('f(y',f(z',f(x',z)))', D3, R3, P[], S{x14 -> y', x15 -> z', x16 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 26 => ('f(z,f(f(x',y'),z'))', D3, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 27 => ('f(f(x',y'),f(z,z'))', D3, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 28 => ('f(f(y',z),f(z',x'))', D3, R3, P[], S{x14 -> f(y',z), x15 -> z', x16 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 29 => ('f(z',f(f(y',z),x'))', D3, R4, P[], S{x17 -> z', x18 -> f(y',z), x19 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 30 => ('f(y',f(f(z,x'),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 31 => ('f(f(z,x'),f(y',z'))', D3, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 32 => ('f(x',f(z',f(y',z)))', D3, R3, P[], S{x14 -> x', x15 -> z', x16 -> f(y',z)}), NR: 'f(x',f(z',f(y',z)))' ID: 33 => ('f(x',f(f(z,z'),y'))', D3, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 34 => ('f(y',f(z,f(z',x')))', D3, R3, P[2], S{x14 -> z, x15 -> z', x16 -> x'}), NR: 'f(z,f(z',x'))' ID: 35 => ('f(f(z,z'),f(x',y'))', D3, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 36 => ('f(y',f(z',f(z,x')))', D3, R4, P[2], S{x17 -> z', x18 -> z, x19 -> x'}), NR: 'f(z',f(z,x'))' ID: 37 => ('f(y',f(f(z,z'),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 38 => ('f(x',f(z,f(z',y')))', D3, R3, P[2], S{x14 -> z, x15 -> z', x16 -> y'}), NR: 'f(z,f(z',y'))' ID: 39 => ('f(f(z,z'),f(y',x'))', D3, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 40 => ('f(x',f(z',f(z,y')))', D3, R4, P[2], S{x17 -> z', x18 -> z, x19 -> y'}), NR: 'f(z',f(z,y'))' ID: 41 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 42 => ('f(z,f(x',f(z',y')))', D3, R3, P[2], S{x14 -> x', x15 -> z', x16 -> y'}), NR: 'f(x',f(z',y'))' ID: 43 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 44 => ('f(z,f(z',f(x',y')))', D3, R4, P[2], S{x17 -> z', x18 -> x', x19 -> y'}), NR: 'f(z',f(x',y'))' ID: 45 => ('f(x',f(f(y',z'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 46 => ('f(z,f(y',f(z',x')))', D3, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 47 => ('f(f(y',z'),f(x',z))', D3, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 48 => ('f(y',f(x',f(z',z)))', D3, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(z',z)}), NR: 'f(y',f(x',f(z',z)))' ID: 49 => ('f(x',f(y',f(z',z)))', D3, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(z',z)}), NR: 'f(x',f(y',f(z',z)))' ID: 50 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 51 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 52 => ('f(f(z,y'),f(z',x'))', D4, R3, P[], S{x14 -> f(z,y'), x15 -> z', x16 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 53 => ('f(z',f(f(z,y'),x'))', D4, R4, P[], S{x17 -> z', x18 -> f(z,y'), x19 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 54 => ('f(z,f(f(y',z'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',z'), x16 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 55 => ('f(f(y',z'),f(z,x'))', D4, R4, P[], S{x17 -> f(y',z'), x18 -> z, x19 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 56 => ('f(f(x',y'),f(z',z))', D4, R3, P[], S{x14 -> f(x',y'), x15 -> z', x16 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 57 => ('f(z',f(f(x',y'),z))', D4, R4, P[], S{x17 -> z', x18 -> f(x',y'), x19 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 58 => ('f(f(z,x'),f(z',y'))', D4, R3, P[], S{x14 -> f(z,x'), x15 -> z', x16 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 59 => ('f(z',f(f(z,x'),y'))', D4, R4, P[], S{x17 -> z', x18 -> f(z,x'), x19 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 60 => ('f(z,f(f(z',x'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',x'), x16 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 61 => ('f(f(z',x'),f(z,y'))', D4, R4, P[], S{x17 -> f(z',x'), x18 -> z, x19 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 62 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 63 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 64 => ('f(x',f(f(z',y'),z))', D4, R3, P[], S{x14 -> x', x15 -> f(z',y'), x16 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 65 => ('f(f(z',y'),f(x',z))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> x', x19 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 66 => ('f(y',f(f(z',x'),z))', D4, R3, P[], S{x14 -> y', x15 -> f(z',x'), x16 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 67 => ('f(f(z',x'),f(y',z))', D4, R4, P[], S{x17 -> f(z',x'), x18 -> y', x19 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 68 => ('f(x',f(f(z',z),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z',z), x16 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 69 => ('f(f(z',z),f(x',y'))', D4, R4, P[], S{x17 -> f(z',z), x18 -> x', x19 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 70 => ('f(y',f(f(z',z),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 71 => ('f(f(z',z),f(y',x'))', D4, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' SNodesPath1: f(z,f(x',f(y',z'))) TNodesPath1: SNodesPath2: TNodesPath2: f(z',f(f(y',x'),z)) f(z,f(x',f(y',z'))) ->= f(z,f(x',f(y',z'))) *<- f(z',f(f(y',x'),z)) f(z',f(f(y',x'),z)) ->= f(z',f(f(y',x'),z)) *<- f(z,f(x',f(y',z'))) "Strongly closed critical pair" The problem is confluent. Problem 1.11: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Not overlay, Proper, NW0, N20 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(z,f(x',f(y',z'))) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,0),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,19),(5,20),(5,21),(5,22),(6,15),(6,23),(6,24),(6,25),(7,0),(7,15),(7,26),(7,27),(8,1),(8,2),(8,3),(8,4),(9,13),(9,28),(9,29),(9,30),(10,0),(10,17),(10,31),(10,32),(11,2),(11,6),(11,33),(11,34),(12,2),(12,4),(12,35),(12,36),(13,37),(13,38),(13,39),(13,40),(14,41),(14,42),(14,43),(14,44),(15,5),(15,6),(15,7),(15,8),(16,14),(16,33),(16,45),(16,46),(17,10),(17,12),(17,47),(17,48),(18,4),(18,5),(18,28),(18,49),(19,26),(19,34),(19,50),(19,51),(20,15),(20,24),(20,52),(20,53),(21,4),(21,5),(21,28),(21,49),(22,5),(22,6),(22,54),(22,55),(23,27),(23,49),(23,56),(23,57),(24,20),(24,22),(24,58),(24,59),(25,2),(25,6),(25,33),(25,34),(26,38),(26,40),(26,60),(26,61),(27,42),(27,44),(27,62),(27,63),(28,26),(28,34),(28,50),(28,51),(29,2),(29,20),(29,34),(29,42),(30,9),(30,10),(30,11),(30,12),(31,14),(31,33),(31,64),(31,65),(32,5),(32,10),(32,28),(32,44),(33,27),(33,49),(33,56),(33,57),(34,13),(34,28),(34,29),(34,30),(35,5),(35,6),(35,54),(35,55),(36,12),(36,13),(36,14),(36,22),(37,41),(37,42),(37,43),(37,44),(38,26),(38,34),(38,66),(38,67),(39,12),(39,13),(39,14),(39,22),(40,13),(40,28),(40,68),(40,69),(41,37),(41,38),(41,39),(41,40),(42,27),(42,49),(42,70),(42,71),(43,0),(43,13),(43,14),(43,15),(44,14),(44,33),(44,64),(44,65),(45,4),(45,24),(45,38),(45,49),(46,0),(46,16),(46,17),(46,18),(47,13),(47,28),(47,68),(47,69),(48,6),(48,17),(48,33),(48,40),(49,14),(49,33),(49,45),(49,46),(50,5),(50,10),(50,28),(50,44),(51,19),(51,20),(51,21),(51,22),(52,27),(52,49),(52,70),(52,71),(53,2),(53,20),(53,34),(53,42),(54,2),(54,4),(54,35),(54,36),(55,12),(55,22),(55,26),(55,27),(56,6),(56,17),(56,33),(56,40),(57,15),(57,23),(57,24),(57,25),(58,26),(58,34),(58,66),(58,67),(59,4),(59,24),(59,38),(59,49),(60,42),(60,44),(60,62),(60,63),(61,12),(61,22),(61,26),(61,27),(62,38),(62,40),(62,60),(62,61),(63,0),(63,15),(63,26),(63,27),(64,10),(64,24),(64,38),(64,44),(65,0),(65,17),(65,31),(65,32),(66,20),(66,22),(66,58),(66,59),(67,10),(67,24),(67,38),(67,44),(68,10),(68,12),(68,47),(68,48),(69,17),(69,20),(69,40),(69,42),(70,15),(70,24),(70,52),(70,53),(71,17),(71,20),(71,40),(71,42)] ID: 0 => ('f(z,f(x',f(y',z')))', D0) ID: 1 => ('f(x',f(f(y',z'),z))', D1, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 2 => ('f(z,f(y',f(z',x')))', D1, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 3 => ('f(f(y',z'),f(x',z))', D1, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 4 => ('f(z,f(z',f(y',x')))', D1, R4, P[2], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 5 => ('f(x',f(y',f(z',z)))', D2, R1, P[2], S{x8 -> y', x9 -> z', x10 -> z}), NR: 'f(y',f(z',z))' ID: 6 => ('f(x',f(z',f(y',z)))', D2, R2, P[2], S{x11 -> z', x12 -> y', x13 -> z}), NR: 'f(z',f(y',z))' ID: 7 => ('f(f(y',z'),f(z,x'))', D2, R3, P[], S{x14 -> f(y',z'), x15 -> z, x16 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 8 => ('f(z,f(f(y',z'),x'))', D2, R4, P[], S{x17 -> z, x18 -> f(y',z'), x19 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 9 => ('f(y',f(f(z',x'),z))', D2, R3, P[], S{x14 -> y', x15 -> f(z',x'), x16 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 10 => ('f(z,f(z',f(x',y')))', D2, R3, P[2], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 11 => ('f(f(z',x'),f(y',z))', D2, R4, P[], S{x17 -> f(z',x'), x18 -> y', x19 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 12 => ('f(z,f(x',f(z',y')))', D2, R4, P[2], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 13 => ('f(y',f(z',f(x',z)))', D2, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 14 => ('f(z',f(y',f(x',z)))', D2, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(x',z)}), NR: 'f(z',f(y',f(x',z)))' ID: 15 => ('f(x',f(z,f(y',z')))', D2, R3, P[], S{x14 -> x', x15 -> z, x16 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 16 => ('f(z',f(f(y',x'),z))', D2, R3, P[], S{x14 -> z', x15 -> f(y',x'), x16 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 17 => ('f(z,f(y',f(x',z')))', D2, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R4, P[], S{x17 -> f(y',x'), x18 -> z', x19 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(y',f(f(z',z),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 20 => ('f(x',f(z',f(z,y')))', D3, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 21 => ('f(f(z',z),f(y',x'))', D3, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 22 => ('f(x',f(z,f(z',y')))', D3, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 23 => ('f(z',f(f(y',z),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 24 => ('f(x',f(y',f(z,z')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> z'}), NR: 'f(y',f(z,z'))' ID: 25 => ('f(f(y',z),f(z',x'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 26 => ('f(y',f(z',f(z,x')))', D3, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(z,x')}), NR: 'f(y',f(z',f(z,x')))' ID: 27 => ('f(z',f(y',f(z,x')))', D3, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(z,x')}), NR: 'f(z',f(y',f(z,x')))' ID: 28 => ('f(y',f(x',f(z',z)))', D3, R2, P[2], S{x11 -> x', x12 -> z', x13 -> z}), NR: 'f(x',f(z',z))' ID: 29 => ('f(f(z',x'),f(z,y'))', D3, R3, P[], S{x14 -> f(z',x'), x15 -> z, x16 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 30 => ('f(z,f(f(z',x'),y'))', D3, R4, P[], S{x17 -> z, x18 -> f(z',x'), x19 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 31 => ('f(z',f(f(x',y'),z))', D3, R3, P[], S{x14 -> z', x15 -> f(x',y'), x16 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 32 => ('f(f(x',y'),f(z',z))', D3, R4, P[], S{x17 -> f(x',y'), x18 -> z', x19 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 33 => ('f(z',f(x',f(y',z)))', D3, R1, P[], S{x8 -> z', x9 -> x', x10 -> f(y',z)}), NR: 'f(z',f(x',f(y',z)))' ID: 34 => ('f(y',f(z,f(z',x')))', D3, R3, P[], S{x14 -> y', x15 -> z, x16 -> f(z',x')}), NR: 'f(y',f(z,f(z',x')))' ID: 35 => ('f(x',f(f(z',y'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(z',y'), x16 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 36 => ('f(f(z',y'),f(x',z))', D3, R4, P[], S{x17 -> f(z',y'), x18 -> x', x19 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 37 => ('f(z',f(f(x',z),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 38 => ('f(y',f(x',f(z,z')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> z'}), NR: 'f(x',f(z,z'))' ID: 39 => ('f(f(x',z),f(z',y'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 40 => ('f(y',f(z,f(x',z')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> z'}), NR: 'f(z,f(x',z'))' ID: 41 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 42 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 43 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 44 => ('f(z',f(z,f(x',y')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 45 => ('f(f(y',x'),f(z,z'))', D3, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 46 => ('f(z,f(f(y',x'),z'))', D3, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 47 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 48 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 49 => ('f(z',f(z,f(y',x')))', D3, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 50 => ('f(f(z',z),f(x',y'))', D4, R3, P[], S{x14 -> f(z',z), x15 -> x', x16 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 51 => ('f(x',f(f(z',z),y'))', D4, R4, P[], S{x17 -> x', x18 -> f(z',z), x19 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 52 => ('f(z',f(f(z,y'),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 53 => ('f(f(z,y'),f(z',x'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 54 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 55 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 56 => ('f(f(y',z),f(x',z'))', D4, R3, P[], S{x14 -> f(y',z), x15 -> x', x16 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 57 => ('f(x',f(f(y',z),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(y',z), x19 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 58 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 59 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 60 => ('f(z',f(f(z,x'),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 61 => ('f(f(z,x'),f(z',y'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 62 => ('f(y',f(f(z,x'),z'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 63 => ('f(f(z,x'),f(y',z'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 64 => ('f(f(x',y'),f(z,z'))', D4, R3, P[], S{x14 -> f(x',y'), x15 -> z, x16 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 65 => ('f(z,f(f(x',y'),z'))', D4, R4, P[], S{x17 -> z, x18 -> f(x',y'), x19 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 66 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 67 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 68 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 69 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 70 => ('f(x',f(f(z,y'),z'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 71 => ('f(f(z,y'),f(x',z'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' t: f(f(y',x'),f(z',z)) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,13),(3,14),(3,15),(3,16),(4,0),(4,17),(4,18),(4,19),(5,9),(5,10),(5,11),(5,12),(6,20),(6,21),(6,22),(6,23),(7,1),(7,2),(7,24),(7,25),(8,1),(8,26),(8,27),(8,28),(9,5),(9,6),(9,7),(9,8),(10,29),(10,30),(10,31),(10,32),(11,1),(11,2),(11,3),(11,4),(12,2),(12,33),(12,34),(12,35),(13,0),(13,17),(13,18),(13,19),(14,24),(14,36),(14,37),(14,38),(15,3),(15,4),(15,23),(15,32),(16,3),(16,39),(16,40),(16,41),(17,13),(17,14),(17,15),(17,16),(18,25),(18,42),(18,43),(18,44),(19,4),(19,45),(19,46),(19,47),(20,24),(20,37),(20,48),(20,49),(21,1),(21,27),(21,50),(21,51),(22,6),(22,12),(22,40),(22,43),(23,6),(23,8),(23,52),(23,53),(24,14),(24,16),(24,54),(24,55),(25,18),(25,19),(25,56),(25,57),(26,25),(26,43),(26,58),(26,59),(27,21),(27,23),(27,60),(27,61),(28,8),(28,10),(28,37),(28,46),(29,3),(29,40),(29,62),(29,63),(30,2),(30,34),(30,64),(30,65),(31,8),(31,10),(31,37),(31,46),(32,10),(32,12),(32,66),(32,67),(33,4),(33,46),(33,68),(33,69),(34,30),(34,32),(34,70),(34,71),(35,6),(35,12),(35,40),(35,43),(36,21),(36,23),(36,60),(36,61),(37,3),(37,40),(37,62),(37,63),(38,14),(38,19),(38,27),(38,30),(39,30),(39,32),(39,70),(39,71),(40,24),(40,37),(40,48),(40,49),(41,16),(41,18),(41,21),(41,34),(42,1),(42,27),(42,50),(42,51),(43,4),(43,46),(43,68),(43,69),(44,16),(44,18),(44,21),(44,34),(45,2),(45,34),(45,64),(45,65),(46,25),(46,43),(46,58),(46,59),(47,14),(47,19),(47,27),(47,30),(48,6),(48,19),(48,30),(48,40),(49,20),(49,21),(49,22),(49,23),(50,25),(50,42),(50,43),(50,44),(51,10),(51,18),(51,21),(51,37),(52,10),(52,12),(52,66),(52,67),(53,23),(53,24),(53,25),(53,32),(54,18),(54,19),(54,56),(54,57),(55,23),(55,24),(55,25),(55,32),(56,14),(56,16),(56,54),(56,55),(57,1),(57,2),(57,24),(57,25),(58,8),(58,16),(58,34),(58,46),(59,1),(59,26),(59,27),(59,28),(60,24),(60,36),(60,37),(60,38),(61,12),(61,14),(61,27),(61,43),(62,10),(62,18),(62,21),(62,37),(63,29),(63,30),(63,31),(63,32),(64,4),(64,45),(64,46),(64,47),(65,6),(65,19),(65,30),(65,40),(66,6),(66,8),(66,52),(66,53),(67,3),(67,4),(67,23),(67,32),(68,12),(68,14),(68,27),(68,43),(69,2),(69,33),(69,34),(69,35),(70,3),(70,39),(70,40),(70,41),(71,8),(71,16),(71,34),(71,46)] ID: 0 => ('f(f(y',x'),f(z',z))', D0) ID: 1 => ('f(y',f(x',f(z',z)))', D1, R1, P[], S{x8 -> y', x9 -> x', x10 -> f(z',z)}), NR: 'f(y',f(x',f(z',z)))' ID: 2 => ('f(x',f(y',f(z',z)))', D1, R2, P[], S{x11 -> x', x12 -> y', x13 -> f(z',z)}), NR: 'f(x',f(y',f(z',z)))' ID: 3 => ('f(z',f(z,f(y',x')))', D1, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 4 => ('f(z,f(z',f(y',x')))', D1, R4, P[], S{x17 -> z, x18 -> z', x19 -> f(y',x')}), NR: 'f(z,f(z',f(y',x')))' ID: 5 => ('f(x',f(f(z',z),y'))', D2, R3, P[], S{x14 -> x', x15 -> f(z',z), x16 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 6 => ('f(y',f(z',f(z,x')))', D2, R3, P[2], S{x14 -> z', x15 -> z, x16 -> x'}), NR: 'f(z',f(z,x'))' ID: 7 => ('f(f(z',z),f(x',y'))', D2, R4, P[], S{x17 -> f(z',z), x18 -> x', x19 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 8 => ('f(y',f(z,f(z',x')))', D2, R4, P[2], S{x17 -> z, x18 -> z', x19 -> x'}), NR: 'f(z,f(z',x'))' ID: 9 => ('f(y',f(f(z',z),x'))', D2, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 10 => ('f(x',f(z',f(z,y')))', D2, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 11 => ('f(f(z',z),f(y',x'))', D2, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 12 => ('f(x',f(z,f(z',y')))', D2, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 13 => ('f(z,f(f(y',x'),z'))', D2, R3, P[], S{x14 -> z, x15 -> f(y',x'), x16 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 14 => ('f(z',f(y',f(x',z)))', D2, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z}), NR: 'f(y',f(x',z))' ID: 15 => ('f(f(y',x'),f(z,z'))', D2, R4, P[], S{x17 -> f(y',x'), x18 -> z, x19 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 16 => ('f(z',f(x',f(y',z)))', D2, R4, P[2], S{x17 -> x', x18 -> y', x19 -> z}), NR: 'f(x',f(y',z))' ID: 17 => ('f(z',f(f(y',x'),z))', D2, R3, P[], S{x14 -> z', x15 -> f(y',x'), x16 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 18 => ('f(z,f(y',f(x',z')))', D2, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 19 => ('f(z,f(x',f(y',z')))', D2, R4, P[2], S{x17 -> x', x18 -> y', x19 -> z'}), NR: 'f(x',f(y',z'))' ID: 20 => ('f(z',f(f(z,x'),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 21 => ('f(y',f(z,f(x',z')))', D3, R3, P[2], S{x14 -> z, x15 -> x', x16 -> z'}), NR: 'f(z,f(x',z'))' ID: 22 => ('f(f(z,x'),f(z',y'))', D3, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 23 => ('f(y',f(x',f(z,z')))', D3, R4, P[2], S{x17 -> x', x18 -> z, x19 -> z'}), NR: 'f(x',f(z,z'))' ID: 24 => ('f(z',f(z,f(x',y')))', D3, R1, P[], S{x8 -> z', x9 -> z, x10 -> f(x',y')}), NR: 'f(z',f(z,f(x',y')))' ID: 25 => ('f(z,f(z',f(x',y')))', D3, R2, P[], S{x11 -> z, x12 -> z', x13 -> f(x',y')}), NR: 'f(z,f(z',f(x',y')))' ID: 26 => ('f(z,f(f(z',x'),y'))', D3, R3, P[], S{x14 -> z, x15 -> f(z',x'), x16 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 27 => ('f(y',f(z',f(x',z)))', D3, R3, P[2], S{x14 -> z', x15 -> x', x16 -> z}), NR: 'f(z',f(x',z))' ID: 28 => ('f(f(z',x'),f(z,y'))', D3, R4, P[], S{x17 -> f(z',x'), x18 -> z, x19 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 29 => ('f(z',f(f(z,y'),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 30 => ('f(x',f(z,f(y',z')))', D3, R3, P[2], S{x14 -> z, x15 -> y', x16 -> z'}), NR: 'f(z,f(y',z'))' ID: 31 => ('f(f(z,y'),f(z',x'))', D3, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 32 => ('f(x',f(y',f(z,z')))', D3, R4, P[2], S{x17 -> y', x18 -> z, x19 -> z'}), NR: 'f(y',f(z,z'))' ID: 33 => ('f(z,f(f(z',y'),x'))', D3, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 34 => ('f(x',f(z',f(y',z)))', D3, R3, P[2], S{x14 -> z', x15 -> y', x16 -> z}), NR: 'f(z',f(y',z))' ID: 35 => ('f(f(z',y'),f(z,x'))', D3, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 36 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 37 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 38 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 39 => ('f(x',f(f(y',z),z'))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z), x16 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 40 => ('f(z',f(y',f(z,x')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> x'}), NR: 'f(y',f(z,x'))' ID: 41 => ('f(f(y',z),f(x',z'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> x', x19 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 42 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 43 => ('f(z,f(x',f(z',y')))', D3, R3, P[2], S{x14 -> x', x15 -> z', x16 -> y'}), NR: 'f(x',f(z',y'))' ID: 44 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 45 => ('f(x',f(f(y',z'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 46 => ('f(z,f(y',f(z',x')))', D3, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 47 => ('f(f(y',z'),f(x',z))', D3, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 48 => ('f(f(z,x'),f(y',z'))', D4, R3, P[], S{x14 -> f(z,x'), x15 -> y', x16 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 49 => ('f(y',f(f(z,x'),z'))', D4, R4, P[], S{x17 -> y', x18 -> f(z,x'), x19 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 50 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 51 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 52 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 53 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 54 => ('f(z,f(f(x',y'),z'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 55 => ('f(f(x',y'),f(z,z'))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 56 => ('f(z',f(f(x',y'),z))', D4, R3, P[], S{x14 -> z', x15 -> f(x',y'), x16 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 57 => ('f(f(x',y'),f(z',z))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> z', x19 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 58 => ('f(f(z',x'),f(y',z))', D4, R3, P[], S{x14 -> f(z',x'), x15 -> y', x16 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 59 => ('f(y',f(f(z',x'),z))', D4, R4, P[], S{x17 -> y', x18 -> f(z',x'), x19 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 60 => ('f(z',f(f(x',z),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 61 => ('f(f(x',z),f(z',y'))', D4, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 62 => ('f(f(z,y'),f(x',z'))', D4, R3, P[], S{x14 -> f(z,y'), x15 -> x', x16 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 63 => ('f(x',f(f(z,y'),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(z,y'), x19 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 64 => ('f(z,f(f(y',z'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',z'), x16 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 65 => ('f(f(y',z'),f(z,x'))', D4, R4, P[], S{x17 -> f(y',z'), x18 -> z, x19 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 66 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 67 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 68 => ('f(f(z',y'),f(x',z))', D4, R3, P[], S{x14 -> f(z',y'), x15 -> x', x16 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 69 => ('f(x',f(f(z',y'),z))', D4, R4, P[], S{x17 -> x', x18 -> f(z',y'), x19 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 70 => ('f(z',f(f(y',z),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 71 => ('f(f(y',z),f(z',x'))', D4, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' SNodesPath1: f(z,f(x',f(y',z'))) TNodesPath1: f(f(y',x'),f(z',z)) -> f(y',f(x',f(z',z))) -> f(x',f(f(z',z),y')) -> f(y',f(f(z',z),x')) -> f(y',f(z',f(z,x'))) -> f(z',f(f(z,x'),y')) -> f(z',f(z,f(x',y'))) -> f(z',f(y',f(x',z))) -> f(y',f(f(x',z),z')) -> f(y',f(z,f(x',z'))) -> f(y',f(z',f(x',z))) -> f(y',f(x',f(z,z'))) -> f(y',f(z,f(z',x'))) -> f(z,f(f(z',x'),y')) -> f(z,f(z',f(x',y'))) -> f(z,f(y',f(x',z'))) -> f(y',f(f(x',z'),z)) -> f(z,f(f(x',z'),y')) -> f(z,f(x',f(z',y'))) -> f(z,f(z',f(y',x'))) -> f(z',f(f(y',x'),z)) -> f(z,f(f(y',x'),z')) -> f(z,f(x',f(y',z'))) SNodesPath2: TNodesPath2: f(f(y',x'),f(z',z)) f(z,f(x',f(y',z'))) ->= f(z,f(x',f(y',z'))) *<- f(f(y',x'),f(z',z)) f(f(y',x'),f(z',z)) ->= f(f(y',x'),f(z',z)) *<- f(z,f(x',f(y',z'))) "Strongly closed critical pair" The problem is confluent. Problem 1.12: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Overlay, Proper, NW0, N21 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(x',f(y',z')) Nodes: [0,1,2,3,4,5] Edges: [(0,1),(0,2),(1,3),(1,4),(2,0),(2,5),(3,0),(3,5),(4,1),(4,2),(5,3),(5,4)] ID: 0 => ('f(x',f(y',z'))', D0) ID: 1 => ('f(y',f(z',x'))', D1, R3, P[], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 2 => ('f(z',f(y',x'))', D1, R4, P[], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 3 => ('f(z',f(x',y'))', D2, R3, P[], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 4 => ('f(x',f(z',y'))', D2, R4, P[], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 5 => ('f(y',f(x',z'))', D2, R3, P[], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' t: f(y',f(x',z')) Nodes: [0,1,2,3,4,5] Edges: [(0,1),(0,2),(1,3),(1,4),(2,0),(2,5),(3,0),(3,5),(4,1),(4,2),(5,3),(5,4)] ID: 0 => ('f(y',f(x',z'))', D0) ID: 1 => ('f(x',f(z',y'))', D1, R3, P[], S{x14 -> x', x15 -> z', x16 -> y'}), NR: 'f(x',f(z',y'))' ID: 2 => ('f(z',f(x',y'))', D1, R4, P[], S{x17 -> z', x18 -> x', x19 -> y'}), NR: 'f(z',f(x',y'))' ID: 3 => ('f(z',f(y',x'))', D2, R3, P[], S{x14 -> z', x15 -> y', x16 -> x'}), NR: 'f(z',f(y',x'))' ID: 4 => ('f(y',f(z',x'))', D2, R4, P[], S{x17 -> y', x18 -> z', x19 -> x'}), NR: 'f(y',f(z',x'))' ID: 5 => ('f(x',f(y',z'))', D2, R3, P[], S{x14 -> x', x15 -> y', x16 -> z'}), NR: 'f(x',f(y',z'))' SNodesPath1: f(x',f(y',z')) TNodesPath1: f(y',f(x',z')) -> f(x',f(z',y')) -> f(z',f(y',x')) -> f(x',f(y',z')) SNodesPath2: f(x',f(y',z')) -> f(y',f(z',x')) -> f(z',f(x',y')) -> f(y',f(x',z')) TNodesPath2: f(y',f(x',z')) f(x',f(y',z')) ->= f(x',f(y',z')) *<- f(y',f(x',z')) f(y',f(x',z')) ->= f(y',f(x',z')) *<- f(x',f(y',z')) "Strongly closed critical pair" The problem is confluent. Problem 1.13: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Confluence Problem: (VAR x y z x' y' z') (REPLACEMENT-MAP (f 1, 2) (fSNonEmpty) ) (RULES f(f(x,y),z) -> f(x,f(y,z)) f(f(y,x),z) -> f(x,f(y,z)) f(z,f(x,y)) -> f(x,f(y,z)) f(z,f(y,x)) -> f(x,f(y,z)) ) Critical Pairs: => Not trivial, Not overlay, Proper, NW0, N22 Linear:YES ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Strong Confluence Procedure: -> Rewritings: s: f(f(x',f(y',z')),z) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,13),(3,14),(3,15),(3,16),(4,0),(4,17),(4,18),(4,19),(5,20),(5,21),(5,22),(5,23),(6,11),(6,24),(6,25),(6,26),(7,11),(7,12),(7,27),(7,28),(8,1),(8,2),(8,29),(8,30),(9,31),(9,32),(9,33),(9,34),(10,35),(10,36),(10,37),(10,38),(11,5),(11,6),(11,7),(11,8),(12,1),(12,2),(12,29),(12,30),(13,9),(13,39),(13,40),(13,41),(14,6),(14,29),(14,42),(14,43),(15,0),(15,19),(15,44),(15,45),(16,3),(16,4),(16,46),(16,47),(17,10),(17,42),(17,48),(17,49),(18,5),(18,30),(18,39),(18,50),(19,15),(19,16),(19,51),(19,52),(20,27),(20,43),(20,53),(20,54),(21,11),(21,25),(21,55),(21,56),(22,5),(22,30),(22,39),(22,50),(23,5),(23,6),(23,57),(23,58),(24,28),(24,50),(24,59),(24,60),(25,21),(25,23),(25,61),(25,62),(26,6),(26,29),(26,42),(26,43),(27,32),(27,34),(27,63),(27,64),(28,36),(28,38),(28,65),(28,66),(29,13),(29,14),(29,67),(29,68),(30,12),(30,17),(30,18),(30,69),(31,35),(31,36),(31,37),(31,38),(32,27),(32,43),(32,70),(32,71),(33,9),(33,10),(33,23),(33,68),(34,9),(34,39),(34,72),(34,73),(35,31),(35,32),(35,33),(35,34),(36,28),(36,50),(36,74),(36,75),(37,9),(37,10),(37,11),(37,12),(38,10),(38,42),(38,76),(38,77),(39,27),(39,43),(39,53),(39,54),(40,21),(40,29),(40,36),(40,43),(41,13),(41,14),(41,67),(41,68),(42,28),(42,50),(42,59),(42,60),(43,9),(43,39),(43,40),(43,41),(44,10),(44,42),(44,76),(44,77),(45,5),(45,38),(45,39),(45,67),(46,5),(46,6),(46,57),(46,58),(47,9),(47,10),(47,23),(47,68),(48,25),(48,30),(48,32),(48,50),(49,12),(49,17),(49,18),(49,69),(50,10),(50,42),(50,48),(50,49),(51,9),(51,39),(51,72),(51,73),(52,6),(52,34),(52,42),(52,69),(53,5),(53,38),(53,39),(53,67),(54,20),(54,21),(54,22),(54,23),(55,28),(55,50),(55,74),(55,75),(56,21),(56,29),(56,36),(56,43),(57,29),(57,30),(57,46),(57,47),(58,23),(58,27),(58,28),(58,68),(59,6),(59,34),(59,42),(59,69),(60,11),(60,24),(60,25),(60,26),(61,27),(61,43),(61,70),(61,71),(62,25),(62,30),(62,32),(62,50),(63,36),(63,38),(63,65),(63,66),(64,23),(64,27),(64,28),(64,68),(65,32),(65,34),(65,63),(65,64),(66,11),(66,12),(66,27),(66,28),(67,12),(67,44),(67,45),(67,69),(68,29),(68,30),(68,46),(68,47),(69,51),(69,52),(69,67),(69,68),(70,21),(70,23),(70,61),(70,62),(71,25),(71,32),(71,38),(71,67),(72,51),(72,52),(72,67),(72,68),(73,21),(73,34),(73,36),(73,69),(74,11),(74,25),(74,55),(74,56),(75,21),(75,34),(75,36),(75,69),(76,12),(76,44),(76,45),(76,69),(77,25),(77,32),(77,38),(77,67)] ID: 0 => ('f(f(x',f(y',z')),z)', D0) ID: 1 => ('f(x',f(f(y',z'),z))', D1, R1, P[], S{x8 -> x', x9 -> f(y',z'), x10 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 2 => ('f(f(y',z'),f(x',z))', D1, R2, P[], S{x11 -> f(y',z'), x12 -> x', x13 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 3 => ('f(f(y',f(z',x')),z)', D1, R3, P[1], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 4 => ('f(f(z',f(y',x')),z)', D1, R4, P[1], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 5 => ('f(x',f(y',f(z',z)))', D2, R1, P[2], S{x8 -> y', x9 -> z', x10 -> z}), NR: 'f(y',f(z',z))' ID: 6 => ('f(x',f(z',f(y',z)))', D2, R2, P[2], S{x11 -> z', x12 -> y', x13 -> z}), NR: 'f(z',f(y',z))' ID: 7 => ('f(f(y',z'),f(z,x'))', D2, R3, P[], S{x14 -> f(y',z'), x15 -> z, x16 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 8 => ('f(z,f(f(y',z'),x'))', D2, R4, P[], S{x17 -> z, x18 -> f(y',z'), x19 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 9 => ('f(y',f(z',f(x',z)))', D2, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 10 => ('f(z',f(y',f(x',z)))', D2, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(x',z)}), NR: 'f(z',f(y',f(x',z)))' ID: 11 => ('f(x',f(z,f(y',z')))', D2, R3, P[], S{x14 -> x', x15 -> z, x16 -> f(y',z')}), NR: 'f(x',f(z,f(y',z')))' ID: 12 => ('f(z,f(x',f(y',z')))', D2, R4, P[], S{x17 -> z, x18 -> x', x19 -> f(y',z')}), NR: 'f(z,f(x',f(y',z')))' ID: 13 => ('f(y',f(f(z',x'),z))', D2, R1, P[], S{x8 -> y', x9 -> f(z',x'), x10 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 14 => ('f(f(z',x'),f(y',z))', D2, R2, P[], S{x11 -> f(z',x'), x12 -> y', x13 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 15 => ('f(f(z',f(x',y')),z)', D2, R3, P[1], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 16 => ('f(f(x',f(z',y')),z)', D2, R4, P[1], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 17 => ('f(z',f(f(y',x'),z))', D2, R1, P[], S{x8 -> z', x9 -> f(y',x'), x10 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 18 => ('f(f(y',x'),f(z',z))', D2, R2, P[], S{x11 -> f(y',x'), x12 -> z', x13 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 19 => ('f(f(y',f(x',z')),z)', D2, R3, P[1], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 20 => ('f(y',f(f(z',z),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 21 => ('f(x',f(z',f(z,y')))', D3, R3, P[2], S{x14 -> z', x15 -> z, x16 -> y'}), NR: 'f(z',f(z,y'))' ID: 22 => ('f(f(z',z),f(y',x'))', D3, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 23 => ('f(x',f(z,f(z',y')))', D3, R4, P[2], S{x17 -> z, x18 -> z', x19 -> y'}), NR: 'f(z,f(z',y'))' ID: 24 => ('f(z',f(f(y',z),x'))', D3, R3, P[], S{x14 -> z', x15 -> f(y',z), x16 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 25 => ('f(x',f(y',f(z,z')))', D3, R3, P[2], S{x14 -> y', x15 -> z, x16 -> z'}), NR: 'f(y',f(z,z'))' ID: 26 => ('f(f(y',z),f(z',x'))', D3, R4, P[], S{x17 -> f(y',z), x18 -> z', x19 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 27 => ('f(y',f(z',f(z,x')))', D3, R1, P[], S{x8 -> y', x9 -> z', x10 -> f(z,x')}), NR: 'f(y',f(z',f(z,x')))' ID: 28 => ('f(z',f(y',f(z,x')))', D3, R2, P[], S{x11 -> z', x12 -> y', x13 -> f(z,x')}), NR: 'f(z',f(y',f(z,x')))' ID: 29 => ('f(z,f(y',f(z',x')))', D3, R1, P[2], S{x8 -> y', x9 -> z', x10 -> x'}), NR: 'f(y',f(z',x'))' ID: 30 => ('f(z,f(z',f(y',x')))', D3, R2, P[2], S{x11 -> z', x12 -> y', x13 -> x'}), NR: 'f(z',f(y',x'))' ID: 31 => ('f(z',f(f(x',z),y'))', D3, R3, P[], S{x14 -> z', x15 -> f(x',z), x16 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 32 => ('f(y',f(x',f(z,z')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> z'}), NR: 'f(x',f(z,z'))' ID: 33 => ('f(f(x',z),f(z',y'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> z', x19 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 34 => ('f(y',f(z,f(x',z')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> z'}), NR: 'f(z,f(x',z'))' ID: 35 => ('f(y',f(f(x',z),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 36 => ('f(z',f(x',f(z,y')))', D3, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 37 => ('f(f(x',z),f(y',z'))', D3, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 38 => ('f(z',f(z,f(x',y')))', D3, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 39 => ('f(y',f(x',f(z',z)))', D3, R2, P[2], S{x11 -> x', x12 -> z', x13 -> z}), NR: 'f(x',f(z',z))' ID: 40 => ('f(f(z',x'),f(z,y'))', D3, R3, P[], S{x14 -> f(z',x'), x15 -> z, x16 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 41 => ('f(z,f(f(z',x'),y'))', D3, R4, P[], S{x17 -> z, x18 -> f(z',x'), x19 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 42 => ('f(z',f(x',f(y',z)))', D3, R1, P[], S{x8 -> z', x9 -> x', x10 -> f(y',z)}), NR: 'f(z',f(x',f(y',z)))' ID: 43 => ('f(y',f(z,f(z',x')))', D3, R3, P[], S{x14 -> y', x15 -> z, x16 -> f(z',x')}), NR: 'f(y',f(z,f(z',x')))' ID: 44 => ('f(z',f(f(x',y'),z))', D3, R1, P[], S{x8 -> z', x9 -> f(x',y'), x10 -> z}), NR: 'f(z',f(f(x',y'),z))' ID: 45 => ('f(f(x',y'),f(z',z))', D3, R2, P[], S{x11 -> f(x',y'), x12 -> z', x13 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 46 => ('f(x',f(f(z',y'),z))', D3, R1, P[], S{x8 -> x', x9 -> f(z',y'), x10 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 47 => ('f(f(z',y'),f(x',z))', D3, R2, P[], S{x11 -> f(z',y'), x12 -> x', x13 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 48 => ('f(f(y',x'),f(z,z'))', D3, R3, P[], S{x14 -> f(y',x'), x15 -> z, x16 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 49 => ('f(z,f(f(y',x'),z'))', D3, R4, P[], S{x17 -> z, x18 -> f(y',x'), x19 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 50 => ('f(z',f(z,f(y',x')))', D3, R3, P[], S{x14 -> z', x15 -> z, x16 -> f(y',x')}), NR: 'f(z',f(z,f(y',x')))' ID: 51 => ('f(y',f(f(x',z'),z))', D3, R1, P[], S{x8 -> y', x9 -> f(x',z'), x10 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 52 => ('f(f(x',z'),f(y',z))', D3, R2, P[], S{x11 -> f(x',z'), x12 -> y', x13 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 53 => ('f(f(z',z),f(x',y'))', D4, R3, P[], S{x14 -> f(z',z), x15 -> x', x16 -> y'}), NR: 'f(f(z',z),f(x',y'))' ID: 54 => ('f(x',f(f(z',z),y'))', D4, R4, P[], S{x17 -> x', x18 -> f(z',z), x19 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 55 => ('f(z',f(f(z,y'),x'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,y'), x16 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 56 => ('f(f(z,y'),f(z',x'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> z', x19 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 57 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 58 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 59 => ('f(f(y',z),f(x',z'))', D4, R3, P[], S{x14 -> f(y',z), x15 -> x', x16 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 60 => ('f(x',f(f(y',z),z'))', D4, R4, P[], S{x17 -> x', x18 -> f(y',z), x19 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 61 => ('f(y',f(f(z,z'),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 62 => ('f(f(z,z'),f(y',x'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 63 => ('f(z',f(f(z,x'),y'))', D4, R3, P[], S{x14 -> z', x15 -> f(z,x'), x16 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 64 => ('f(f(z,x'),f(z',y'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> z', x19 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 65 => ('f(y',f(f(z,x'),z'))', D4, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 66 => ('f(f(z,x'),f(y',z'))', D4, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 67 => ('f(z,f(z',f(x',y')))', D4, R3, P[2], S{x14 -> z', x15 -> x', x16 -> y'}), NR: 'f(z',f(x',y'))' ID: 68 => ('f(z,f(x',f(z',y')))', D4, R4, P[2], S{x17 -> x', x18 -> z', x19 -> y'}), NR: 'f(x',f(z',y'))' ID: 69 => ('f(z,f(y',f(x',z')))', D4, R3, P[2], S{x14 -> y', x15 -> x', x16 -> z'}), NR: 'f(y',f(x',z'))' ID: 70 => ('f(x',f(f(z,z'),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 71 => ('f(f(z,z'),f(x',y'))', D4, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 72 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 73 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 74 => ('f(x',f(f(z,y'),z'))', D4, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 75 => ('f(f(z,y'),f(x',z'))', D4, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 76 => ('f(z,f(f(x',y'),z'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',y'), x16 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 77 => ('f(f(x',y'),f(z,z'))', D4, R4, P[], S{x17 -> f(x',y'), x18 -> z, x19 -> z'}), NR: 'f(f(x',y'),f(z,z'))' t: f(z',f(f(x',y'),z)) Nodes: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Edges: [(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(1,8),(2,9),(2,10),(2,11),(2,12),(3,12),(3,13),(3,14),(3,15),(4,0),(4,16),(4,17),(4,18),(5,13),(5,19),(5,20),(5,21),(6,10),(6,12),(6,22),(6,23),(7,1),(7,17),(7,24),(7,25),(8,1),(8,2),(8,26),(8,27),(9,14),(9,24),(9,28),(9,29),(10,6),(10,8),(10,30),(10,31),(11,2),(11,16),(11,19),(11,32),(12,1),(12,2),(12,3),(12,4),(13,33),(13,34),(13,35),(13,36),(14,37),(14,38),(14,39),(14,40),(15,0),(15,16),(15,17),(15,18),(16,41),(16,42),(16,43),(16,44),(17,15),(17,45),(17,46),(17,47),(18,12),(18,15),(18,48),(18,49),(19,25),(19,48),(19,50),(19,51),(20,1),(20,25),(20,38),(20,42),(21,5),(21,6),(21,7),(21,8),(22,14),(22,24),(22,52),(22,53),(23,6),(23,16),(23,19),(23,40),(24,32),(24,49),(24,54),(24,55),(25,13),(25,19),(25,20),(25,21),(26,16),(26,17),(26,56),(26,57),(27,8),(27,13),(27,14),(27,44),(28,2),(28,32),(28,34),(28,46),(29,9),(29,10),(29,11),(29,12),(30,13),(30,19),(30,58),(30,59),(31,10),(31,17),(31,24),(31,36),(32,14),(32,24),(32,28),(32,29),(33,37),(33,38),(33,39),(33,40),(34,25),(34,48),(34,60),(34,61),(35,8),(35,13),(35,14),(35,44),(36,13),(36,19),(36,58),(36,59),(37,33),(37,34),(37,35),(37,36),(38,32),(38,49),(38,62),(38,63),(39,12),(39,13),(39,14),(39,15),(40,14),(40,24),(40,52),(40,53),(41,25),(41,48),(41,50),(41,51),(42,15),(42,46),(42,64),(42,65),(43,2),(43,16),(43,19),(43,32),(44,16),(44,17),(44,56),(44,57),(45,32),(45,49),(45,54),(45,55),(46,42),(46,44),(46,66),(46,67),(47,1),(47,17),(47,24),(47,25),(48,34),(48,36),(48,68),(48,69),(49,38),(49,40),(49,70),(49,71),(50,41),(50,42),(50,43),(50,44),(51,6),(51,16),(51,19),(51,40),(52,6),(52,34),(52,40),(52,46),(53,10),(53,12),(53,22),(53,23),(54,15),(54,45),(54,46),(54,47),(55,10),(55,17),(55,24),(55,36),(56,8),(56,44),(56,48),(56,49),(57,1),(57,2),(57,26),(57,27),(58,10),(58,36),(58,38),(58,42),(59,6),(59,8),(59,30),(59,31),(60,42),(60,44),(60,66),(60,67),(61,6),(61,34),(61,40),(61,46),(62,15),(62,46),(62,64),(62,65),(63,10),(63,36),(63,38),(63,42),(64,32),(64,49),(64,62),(64,63),(65,1),(65,25),(65,38),(65,42),(66,25),(66,48),(66,60),(66,61),(67,2),(67,32),(67,34),(67,46),(68,38),(68,40),(68,70),(68,71),(69,8),(69,44),(69,48),(69,49),(70,34),(70,36),(70,68),(70,69),(71,12),(71,15),(71,48),(71,49)] ID: 0 => ('f(z',f(f(x',y'),z))', D0) ID: 1 => ('f(z',f(x',f(y',z)))', D1, R1, P[2], S{x8 -> x', x9 -> y', x10 -> z}), NR: 'f(x',f(y',z))' ID: 2 => ('f(z',f(y',f(x',z)))', D1, R2, P[2], S{x11 -> y', x12 -> x', x13 -> z}), NR: 'f(y',f(x',z))' ID: 3 => ('f(f(x',y'),f(z,z'))', D1, R3, P[], S{x14 -> f(x',y'), x15 -> z, x16 -> z'}), NR: 'f(f(x',y'),f(z,z'))' ID: 4 => ('f(z,f(f(x',y'),z'))', D1, R4, P[], S{x17 -> z, x18 -> f(x',y'), x19 -> z'}), NR: 'f(z,f(f(x',y'),z'))' ID: 5 => ('f(x',f(f(y',z),z'))', D2, R3, P[], S{x14 -> x', x15 -> f(y',z), x16 -> z'}), NR: 'f(x',f(f(y',z),z'))' ID: 6 => ('f(z',f(y',f(z,x')))', D2, R3, P[2], S{x14 -> y', x15 -> z, x16 -> x'}), NR: 'f(y',f(z,x'))' ID: 7 => ('f(f(y',z),f(x',z'))', D2, R4, P[], S{x17 -> f(y',z), x18 -> x', x19 -> z'}), NR: 'f(f(y',z),f(x',z'))' ID: 8 => ('f(z',f(z,f(y',x')))', D2, R4, P[2], S{x17 -> z, x18 -> y', x19 -> x'}), NR: 'f(z,f(y',x'))' ID: 9 => ('f(y',f(f(x',z),z'))', D2, R3, P[], S{x14 -> y', x15 -> f(x',z), x16 -> z'}), NR: 'f(y',f(f(x',z),z'))' ID: 10 => ('f(z',f(x',f(z,y')))', D2, R3, P[2], S{x14 -> x', x15 -> z, x16 -> y'}), NR: 'f(x',f(z,y'))' ID: 11 => ('f(f(x',z),f(y',z'))', D2, R4, P[], S{x17 -> f(x',z), x18 -> y', x19 -> z'}), NR: 'f(f(x',z),f(y',z'))' ID: 12 => ('f(z',f(z,f(x',y')))', D2, R4, P[2], S{x17 -> z, x18 -> x', x19 -> y'}), NR: 'f(z,f(x',y'))' ID: 13 => ('f(x',f(y',f(z,z')))', D2, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(z,z')}), NR: 'f(x',f(y',f(z,z')))' ID: 14 => ('f(y',f(x',f(z,z')))', D2, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(z,z')}), NR: 'f(y',f(x',f(z,z')))' ID: 15 => ('f(z,f(z',f(x',y')))', D2, R3, P[], S{x14 -> z, x15 -> z', x16 -> f(x',y')}), NR: 'f(z,f(z',f(x',y')))' ID: 16 => ('f(z,f(x',f(y',z')))', D2, R1, P[2], S{x8 -> x', x9 -> y', x10 -> z'}), NR: 'f(x',f(y',z'))' ID: 17 => ('f(z,f(y',f(x',z')))', D2, R2, P[2], S{x11 -> y', x12 -> x', x13 -> z'}), NR: 'f(y',f(x',z'))' ID: 18 => ('f(f(x',y'),f(z',z))', D2, R3, P[], S{x14 -> f(x',y'), x15 -> z', x16 -> z}), NR: 'f(f(x',y'),f(z',z))' ID: 19 => ('f(x',f(z,f(y',z')))', D3, R2, P[2], S{x11 -> z, x12 -> y', x13 -> z'}), NR: 'f(z,f(y',z'))' ID: 20 => ('f(f(y',z),f(z',x'))', D3, R3, P[], S{x14 -> f(y',z), x15 -> z', x16 -> x'}), NR: 'f(f(y',z),f(z',x'))' ID: 21 => ('f(z',f(f(y',z),x'))', D3, R4, P[], S{x17 -> z', x18 -> f(y',z), x19 -> x'}), NR: 'f(z',f(f(y',z),x'))' ID: 22 => ('f(y',f(f(z,x'),z'))', D3, R3, P[], S{x14 -> y', x15 -> f(z,x'), x16 -> z'}), NR: 'f(y',f(f(z,x'),z'))' ID: 23 => ('f(f(z,x'),f(y',z'))', D3, R4, P[], S{x17 -> f(z,x'), x18 -> y', x19 -> z'}), NR: 'f(f(z,x'),f(y',z'))' ID: 24 => ('f(y',f(z,f(x',z')))', D3, R1, P[], S{x8 -> y', x9 -> z, x10 -> f(x',z')}), NR: 'f(y',f(z,f(x',z')))' ID: 25 => ('f(x',f(z',f(y',z)))', D3, R3, P[], S{x14 -> x', x15 -> z', x16 -> f(y',z)}), NR: 'f(x',f(z',f(y',z)))' ID: 26 => ('f(z,f(f(y',x'),z'))', D3, R3, P[], S{x14 -> z, x15 -> f(y',x'), x16 -> z'}), NR: 'f(z,f(f(y',x'),z'))' ID: 27 => ('f(f(y',x'),f(z,z'))', D3, R4, P[], S{x17 -> f(y',x'), x18 -> z, x19 -> z'}), NR: 'f(f(y',x'),f(z,z'))' ID: 28 => ('f(f(x',z),f(z',y'))', D3, R3, P[], S{x14 -> f(x',z), x15 -> z', x16 -> y'}), NR: 'f(f(x',z),f(z',y'))' ID: 29 => ('f(z',f(f(x',z),y'))', D3, R4, P[], S{x17 -> z', x18 -> f(x',z), x19 -> y'}), NR: 'f(z',f(f(x',z),y'))' ID: 30 => ('f(x',f(f(z,y'),z'))', D3, R3, P[], S{x14 -> x', x15 -> f(z,y'), x16 -> z'}), NR: 'f(x',f(f(z,y'),z'))' ID: 31 => ('f(f(z,y'),f(x',z'))', D3, R4, P[], S{x17 -> f(z,y'), x18 -> x', x19 -> z'}), NR: 'f(f(z,y'),f(x',z'))' ID: 32 => ('f(y',f(z',f(x',z)))', D3, R3, P[], S{x14 -> y', x15 -> z', x16 -> f(x',z)}), NR: 'f(y',f(z',f(x',z)))' ID: 33 => ('f(y',f(f(z,z'),x'))', D3, R3, P[], S{x14 -> y', x15 -> f(z,z'), x16 -> x'}), NR: 'f(y',f(f(z,z'),x'))' ID: 34 => ('f(x',f(z,f(z',y')))', D3, R3, P[2], S{x14 -> z, x15 -> z', x16 -> y'}), NR: 'f(z,f(z',y'))' ID: 35 => ('f(f(z,z'),f(y',x'))', D3, R4, P[], S{x17 -> f(z,z'), x18 -> y', x19 -> x'}), NR: 'f(f(z,z'),f(y',x'))' ID: 36 => ('f(x',f(z',f(z,y')))', D3, R4, P[2], S{x17 -> z', x18 -> z, x19 -> y'}), NR: 'f(z',f(z,y'))' ID: 37 => ('f(x',f(f(z,z'),y'))', D3, R3, P[], S{x14 -> x', x15 -> f(z,z'), x16 -> y'}), NR: 'f(x',f(f(z,z'),y'))' ID: 38 => ('f(y',f(z,f(z',x')))', D3, R3, P[2], S{x14 -> z, x15 -> z', x16 -> x'}), NR: 'f(z,f(z',x'))' ID: 39 => ('f(f(z,z'),f(x',y'))', D3, R4, P[], S{x17 -> f(z,z'), x18 -> x', x19 -> y'}), NR: 'f(f(z,z'),f(x',y'))' ID: 40 => ('f(y',f(z',f(z,x')))', D3, R4, P[2], S{x17 -> z', x18 -> z, x19 -> x'}), NR: 'f(z',f(z,x'))' ID: 41 => ('f(x',f(f(y',z'),z))', D3, R3, P[], S{x14 -> x', x15 -> f(y',z'), x16 -> z}), NR: 'f(x',f(f(y',z'),z))' ID: 42 => ('f(z,f(y',f(z',x')))', D3, R3, P[2], S{x14 -> y', x15 -> z', x16 -> x'}), NR: 'f(y',f(z',x'))' ID: 43 => ('f(f(y',z'),f(x',z))', D3, R4, P[], S{x17 -> f(y',z'), x18 -> x', x19 -> z}), NR: 'f(f(y',z'),f(x',z))' ID: 44 => ('f(z,f(z',f(y',x')))', D3, R4, P[2], S{x17 -> z', x18 -> y', x19 -> x'}), NR: 'f(z',f(y',x'))' ID: 45 => ('f(y',f(f(x',z'),z))', D3, R3, P[], S{x14 -> y', x15 -> f(x',z'), x16 -> z}), NR: 'f(y',f(f(x',z'),z))' ID: 46 => ('f(z,f(x',f(z',y')))', D3, R3, P[2], S{x14 -> x', x15 -> z', x16 -> y'}), NR: 'f(x',f(z',y'))' ID: 47 => ('f(f(x',z'),f(y',z))', D3, R4, P[], S{x17 -> f(x',z'), x18 -> y', x19 -> z}), NR: 'f(f(x',z'),f(y',z))' ID: 48 => ('f(x',f(y',f(z',z)))', D3, R1, P[], S{x8 -> x', x9 -> y', x10 -> f(z',z)}), NR: 'f(x',f(y',f(z',z)))' ID: 49 => ('f(y',f(x',f(z',z)))', D3, R2, P[], S{x11 -> y', x12 -> x', x13 -> f(z',z)}), NR: 'f(y',f(x',f(z',z)))' ID: 50 => ('f(z,f(f(y',z'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(y',z'), x16 -> x'}), NR: 'f(z,f(f(y',z'),x'))' ID: 51 => ('f(f(y',z'),f(z,x'))', D4, R4, P[], S{x17 -> f(y',z'), x18 -> z, x19 -> x'}), NR: 'f(f(y',z'),f(z,x'))' ID: 52 => ('f(f(z,x'),f(z',y'))', D4, R3, P[], S{x14 -> f(z,x'), x15 -> z', x16 -> y'}), NR: 'f(f(z,x'),f(z',y'))' ID: 53 => ('f(z',f(f(z,x'),y'))', D4, R4, P[], S{x17 -> z', x18 -> f(z,x'), x19 -> y'}), NR: 'f(z',f(f(z,x'),y'))' ID: 54 => ('f(z,f(f(x',z'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(x',z'), x16 -> y'}), NR: 'f(z,f(f(x',z'),y'))' ID: 55 => ('f(f(x',z'),f(z,y'))', D4, R4, P[], S{x17 -> f(x',z'), x18 -> z, x19 -> y'}), NR: 'f(f(x',z'),f(z,y'))' ID: 56 => ('f(f(y',x'),f(z',z))', D4, R3, P[], S{x14 -> f(y',x'), x15 -> z', x16 -> z}), NR: 'f(f(y',x'),f(z',z))' ID: 57 => ('f(z',f(f(y',x'),z))', D4, R4, P[], S{x17 -> z', x18 -> f(y',x'), x19 -> z}), NR: 'f(z',f(f(y',x'),z))' ID: 58 => ('f(f(z,y'),f(z',x'))', D4, R3, P[], S{x14 -> f(z,y'), x15 -> z', x16 -> x'}), NR: 'f(f(z,y'),f(z',x'))' ID: 59 => ('f(z',f(f(z,y'),x'))', D4, R4, P[], S{x17 -> z', x18 -> f(z,y'), x19 -> x'}), NR: 'f(z',f(f(z,y'),x'))' ID: 60 => ('f(z,f(f(z',y'),x'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',y'), x16 -> x'}), NR: 'f(z,f(f(z',y'),x'))' ID: 61 => ('f(f(z',y'),f(z,x'))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> z, x19 -> x'}), NR: 'f(f(z',y'),f(z,x'))' ID: 62 => ('f(z,f(f(z',x'),y'))', D4, R3, P[], S{x14 -> z, x15 -> f(z',x'), x16 -> y'}), NR: 'f(z,f(f(z',x'),y'))' ID: 63 => ('f(f(z',x'),f(z,y'))', D4, R4, P[], S{x17 -> f(z',x'), x18 -> z, x19 -> y'}), NR: 'f(f(z',x'),f(z,y'))' ID: 64 => ('f(y',f(f(z',x'),z))', D4, R3, P[], S{x14 -> y', x15 -> f(z',x'), x16 -> z}), NR: 'f(y',f(f(z',x'),z))' ID: 65 => ('f(f(z',x'),f(y',z))', D4, R4, P[], S{x17 -> f(z',x'), x18 -> y', x19 -> z}), NR: 'f(f(z',x'),f(y',z))' ID: 66 => ('f(x',f(f(z',y'),z))', D4, R3, P[], S{x14 -> x', x15 -> f(z',y'), x16 -> z}), NR: 'f(x',f(f(z',y'),z))' ID: 67 => ('f(f(z',y'),f(x',z))', D4, R4, P[], S{x17 -> f(z',y'), x18 -> x', x19 -> z}), NR: 'f(f(z',y'),f(x',z))' ID: 68 => ('f(y',f(f(z',z),x'))', D4, R3, P[], S{x14 -> y', x15 -> f(z',z), x16 -> x'}), NR: 'f(y',f(f(z',z),x'))' ID: 69 => ('f(f(z',z),f(y',x'))', D4, R4, P[], S{x17 -> f(z',z), x18 -> y', x19 -> x'}), NR: 'f(f(z',z),f(y',x'))' ID: 70 => ('f(x',f(f(z',z),y'))', D4, R3, P[], S{x14 -> x', x15 -> f(z',z), x16 -> y'}), NR: 'f(x',f(f(z',z),y'))' ID: 71 => ('f(f(z',z),f(x',y'))', D4, R4, P[], S{x17 -> f(z',z), x18 -> x', x19 -> y'}), NR: 'f(f(z',z),f(x',y'))' SNodesPath1: f(f(x',f(y',z')),z) -> f(x',f(f(y',z'),z)) TNodesPath1: f(z',f(f(x',y'),z)) -> f(z',f(x',f(y',z))) -> f(x',f(f(y',z),z')) -> f(x',f(y',f(z,z'))) -> f(y',f(f(z,z'),x')) -> f(x',f(f(z,z'),y')) -> f(x',f(z,f(z',y'))) -> f(x',f(z',f(y',z))) -> f(x',f(z,f(y',z'))) -> f(x',f(y',f(z',z))) -> f(x',f(z',f(z,y'))) -> f(f(z,y'),f(z',x')) -> f(z',f(x',f(z,y'))) -> f(z',f(y',f(z,x'))) -> f(z',f(z,f(x',y'))) -> f(z',f(y',f(x',z))) -> f(y',f(f(x',z),z')) -> f(y',f(x',f(z,z'))) -> f(y',f(z,f(z',x'))) -> f(y',f(z',f(x',z))) -> f(y',f(z,f(x',z'))) -> f(y',f(x',f(z',z))) -> f(y',f(z',f(z,x'))) -> f(f(z,x'),f(z',y')) -> f(z,f(x',f(z',y'))) -> f(z,f(y',f(z',x'))) -> f(z,f(z',f(x',y'))) -> f(z,f(x',f(y',z'))) -> f(x',f(f(y',z'),z)) SNodesPath2: TNodesPath2: f(z',f(f(x',y'),z)) f(f(x',f(y',z')),z) ->= f(x',f(f(y',z'),z)) *<- f(z',f(f(x',y'),z)) f(z',f(f(x',y'),z)) ->= f(z',f(f(x',y'),z)) *<- f(f(x',f(y',z')),z) "Strongly closed critical pair" The problem is confluent.