MAYBE (ignored inputs)COMMENT submitted by: Johannes Waldmann Rewrite Rules: [ a(b(?x)) -> c(a(?x)), b(a(?x)) -> a(b(?x)), a(c(?x)) -> b(b(?x)), b(c(?x)) -> c(b(?x)), c(b(?x)) -> b(a(?x)), b(a(?x)) -> c(c(?x)), c(a(?x)) -> b(c(?x)), b(a(?x)) -> c(c(?x)), b(b(?x)) -> c(c(?x)) ] Apply Direct Methods... Inner CPs: [ a(a(b(?x_1))) = c(a(a(?x_1))), a(c(b(?x_3))) = c(a(c(?x_3))), a(c(c(?x_5))) = c(a(a(?x_5))), a(c(c(?x_7))) = c(a(a(?x_7))), a(c(c(?x_8))) = c(a(b(?x_8))), b(c(a(?x))) = a(b(b(?x))), b(b(b(?x_2))) = a(b(c(?x_2))), a(b(a(?x_4))) = b(b(b(?x_4))), a(b(c(?x_6))) = b(b(a(?x_6))), b(b(a(?x_4))) = c(b(b(?x_4))), b(b(c(?x_6))) = c(b(a(?x_6))), c(a(b(?x_1))) = b(a(a(?x_1))), c(c(b(?x_3))) = b(a(c(?x_3))), c(c(c(?x_5))) = b(a(a(?x_5))), c(c(c(?x_7))) = b(a(a(?x_7))), c(c(c(?x_8))) = b(a(b(?x_8))), b(c(a(?x))) = c(c(b(?x))), b(b(b(?x_2))) = c(c(c(?x_2))), c(c(a(?x))) = b(c(b(?x))), c(b(b(?x_2))) = b(c(c(?x_2))), b(c(a(?x))) = c(c(b(?x))), b(b(b(?x_2))) = c(c(c(?x_2))), b(a(b(?x_1))) = c(c(a(?x_1))), b(c(b(?x_3))) = c(c(c(?x_3))), b(c(c(?x_5))) = c(c(a(?x_5))), b(c(c(?x_7))) = c(c(a(?x_7))), b(c(c(?x))) = c(c(b(?x))) ] Outer CPs: [ a(b(?x_1)) = c(c(?x_1)), a(b(?x_1)) = c(c(?x_1)), c(c(?x_5)) = c(c(?x_5)) ] not Overlay, check Termination... unknown/not Terminating unknown Knuth & Bendix Linear unknown Development Closed unknown Strongly Closed unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ a(a(b(?x_2))) = c(a(a(?x_2))), a(c(b(?x_4))) = c(a(c(?x_4))), a(c(c(?x_6))) = c(a(a(?x_6))), a(c(c(?x_9))) = c(a(b(?x_9))), a(b(a(b(?x_2)))) = b(c(a(a(?x_2)))), a(b(c(b(?x_4)))) = b(c(a(c(?x_4)))), a(b(c(c(?x_6)))) = b(c(a(a(?x_6)))), a(b(c(c(?x_9)))) = b(c(a(b(?x_9)))), c(c(a(b(?x_2)))) = b(c(a(a(?x_2)))), c(c(c(b(?x_4)))) = b(c(a(c(?x_4)))), c(c(c(c(?x_6)))) = b(c(a(a(?x_6)))), c(c(c(c(?x_9)))) = b(c(a(b(?x_9)))), b(c(a(b(?x_2)))) = c(c(a(a(?x_2)))), b(c(c(b(?x_4)))) = c(c(a(c(?x_4)))), b(c(c(c(?x_6)))) = c(c(a(a(?x_6)))), b(c(c(c(?x_9)))) = c(c(a(b(?x_9)))), a(b(b(?x))) = b(c(a(?x))), c(c(b(?x))) = b(c(a(?x))), b(c(b(?x))) = c(c(a(?x))), c(c(?x)) = a(b(?x)), b(c(a(?x_2))) = a(b(b(?x_2))), b(b(b(?x_3))) = a(b(c(?x_3))), c(a(c(a(?x_2)))) = a(a(b(b(?x_2)))), c(a(b(b(?x_3)))) = a(a(b(c(?x_3)))), b(a(c(a(?x_2)))) = c(a(b(b(?x_2)))), b(a(b(b(?x_3)))) = c(a(b(c(?x_3)))), c(c(c(a(?x_2)))) = b(a(b(b(?x_2)))), c(c(b(b(?x_3)))) = b(a(b(c(?x_3)))), c(a(a(?x))) = a(a(b(?x))), b(a(a(?x))) = c(a(b(?x))), c(c(a(?x))) = b(a(b(?x))), a(b(a(?x_5))) = b(b(b(?x_5))), a(b(c(?x_7))) = b(b(a(?x_7))), a(b(b(a(?x_5)))) = b(b(b(b(?x_5)))), a(b(b(c(?x_7)))) = b(b(b(a(?x_7)))), c(c(b(a(?x_5)))) = b(b(b(b(?x_5)))), c(c(b(c(?x_7)))) = b(b(b(a(?x_7)))), b(c(b(a(?x_5)))) = c(b(b(b(?x_5)))), b(c(b(c(?x_7)))) = c(b(b(a(?x_7)))), a(b(c(?x))) = b(b(b(?x))), c(c(c(?x))) = b(b(b(?x))), b(c(c(?x))) = c(b(b(?x))), b(b(a(?x_5))) = c(b(b(?x_5))), b(b(c(?x_7))) = c(b(a(?x_7))), c(a(b(a(?x_5)))) = a(c(b(b(?x_5)))), c(a(b(c(?x_7)))) = a(c(b(a(?x_7)))), b(a(b(a(?x_5)))) = c(c(b(b(?x_5)))), b(a(b(c(?x_7)))) = c(c(b(a(?x_7)))), c(c(b(a(?x_5)))) = b(c(b(b(?x_5)))), c(c(b(c(?x_7)))) = b(c(b(a(?x_7)))), c(a(c(?x))) = a(c(b(?x))), b(a(c(?x))) = c(c(b(?x))), c(c(c(?x))) = b(c(b(?x))), c(a(b(?x_3))) = b(a(a(?x_3))), c(c(b(?x_5))) = b(a(c(?x_5))), c(c(c(?x_6))) = b(a(a(?x_6))), c(c(c(?x_9))) = b(a(b(?x_9))), b(b(a(b(?x_3)))) = a(b(a(a(?x_3)))), b(b(c(b(?x_5)))) = a(b(a(c(?x_5)))), b(b(c(c(?x_6)))) = a(b(a(a(?x_6)))), b(b(c(c(?x_9)))) = a(b(a(b(?x_9)))), c(b(a(b(?x_3)))) = b(b(a(a(?x_3)))), c(b(c(b(?x_5)))) = b(b(a(c(?x_5)))), c(b(c(c(?x_6)))) = b(b(a(a(?x_6)))), c(b(c(c(?x_9)))) = b(b(a(b(?x_9)))), b(b(b(?x))) = a(b(a(?x))), c(b(b(?x))) = b(b(a(?x))), a(b(?x)) = c(c(?x)), c(c(?x)) = c(c(?x)), b(c(a(?x_2))) = c(c(b(?x_2))), b(b(b(?x_4))) = c(c(c(?x_4))), c(a(c(a(?x_2)))) = a(c(c(b(?x_2)))), c(a(b(b(?x_4)))) = a(c(c(c(?x_4)))), b(a(c(a(?x_2)))) = c(c(c(b(?x_2)))), b(a(b(b(?x_4)))) = c(c(c(c(?x_4)))), c(c(c(a(?x_2)))) = b(c(c(b(?x_2)))), c(c(b(b(?x_4)))) = b(c(c(c(?x_4)))), c(a(a(?x))) = a(c(c(?x))), b(a(a(?x))) = c(c(c(?x))), c(c(a(?x))) = b(c(c(?x))), c(c(a(?x_2))) = b(c(b(?x_2))), c(b(b(?x_4))) = b(c(c(?x_4))), b(b(c(a(?x_2)))) = a(b(c(b(?x_2)))), b(b(b(b(?x_4)))) = a(b(c(c(?x_4)))), c(b(c(a(?x_2)))) = b(b(c(b(?x_2)))), c(b(b(b(?x_4)))) = b(b(c(c(?x_4)))), b(b(a(?x))) = a(b(c(?x))), c(b(a(?x))) = b(b(c(?x))), b(c(c(?x_1))) = c(c(b(?x_1))), b(a(b(?x_3))) = c(c(a(?x_3))), b(c(b(?x_5))) = c(c(c(?x_5))), b(c(c(?x_7))) = c(c(a(?x_7))), c(c(c(c(?x_1)))) = b(c(c(b(?x_1)))), c(c(a(b(?x_3)))) = b(c(c(a(?x_3)))), c(c(c(b(?x_5)))) = b(c(c(c(?x_5)))), c(c(c(c(?x_7)))) = b(c(c(a(?x_7)))), c(a(c(c(?x_1)))) = a(c(c(b(?x_1)))), c(a(a(b(?x_3)))) = a(c(c(a(?x_3)))), c(a(c(b(?x_5)))) = a(c(c(c(?x_5)))), c(a(c(c(?x_7)))) = a(c(c(a(?x_7)))), b(a(c(c(?x_1)))) = c(c(c(b(?x_1)))), b(a(a(b(?x_3)))) = c(c(c(a(?x_3)))), b(a(c(b(?x_5)))) = c(c(c(c(?x_5)))), b(a(c(c(?x_7)))) = c(c(c(a(?x_7)))), c(c(b(?x))) = b(c(c(?x))), c(a(b(?x))) = a(c(c(?x))), b(a(b(?x))) = c(c(c(?x))) ] unknown Okui (Simultaneous CPs) unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping check Locally Decreasing Diagrams by Rule Labelling... Critical Pair by Rules <1, 0> preceded by [(a,1)] joinable by a reduction of rules <[([(a,1)],0),([],2),([(b,1)],1),([(b,1)],0)], [([],6)]> joinable by a reduction of rules <[([(a,1)],0),([],2)], [([],6),([(b,1)],6),([(b,1)],3),([(b,1)],4)]> joinable by a reduction of rules <[([(a,1)],0),([],2),([],8)], [([],6),([],3),([(c,1)],1),([(c,1)],0)]> joinable by a reduction of rules <[([(a,1)],0),([],2),([],8)], [([],6),([],3),([],4),([],7)]> joinable by a reduction of rules <[([(a,1)],0),([],2),([],8)], [([],6),([],3),([],4),([],5)]> joinable by a reduction of rules <[([(a,1)],0),([(a,1)],6),([(a,1)],3),([(a,1)],4)], [([],6),([],3),([],4),([],1)]> joinable by a reduction of rules <[([(a,1)],0),([(a,1)],6),([],0),([(c,1)],2)], [([],6),([(b,1)],6),([(b,1)],3),([],3)]> Critical Pair by Rules <3, 0> preceded by [(a,1)] joinable by a reduction of rules <[([],2),([(b,1)],8)], [([],6)]> Critical Pair by Rules <5, 0> preceded by [(a,1)] joinable by a reduction of rules <[([],2)], [([],6),([(b,1)],6)]> Critical Pair by Rules <7, 0> preceded by [(a,1)] joinable by a reduction of rules <[([],2)], [([],6),([(b,1)],6)]> Critical Pair by Rules <8, 0> preceded by [(a,1)] joinable by a reduction of rules <[([],2),([(b,1)],3)], [([],6)]> Critical Pair by Rules <0, 1> preceded by [(b,1)] joinable by a reduction of rules <[([],3),([(c,1)],1)], [([],0)]> joinable by a reduction of rules <[([(b,1)],6)], [([(a,1)],8),([],2)]> joinable by a reduction of rules <[([(b,1)],6),([(b,1)],3)], [([],0),([],6)]> Critical Pair by Rules <2, 1> preceded by [(b,1)] joinable by a reduction of rules <[], [([(a,1)],3),([],2)]> joinable by a reduction of rules <[([(b,1)],8)], [([],0),([],6)]> Critical Pair by Rules <4, 2> preceded by [(a,1)] joinable by a reduction of rules <[([],0),([],6),([],3)], [([],8),([(c,1)],4)]> joinable by a reduction of rules <[([(a,1)],7),([],2),([],8)], [([],8),([(c,1)],4),([(c,1)],7)]> joinable by a reduction of rules <[([(a,1)],7),([],2),([],8)], [([],8),([(c,1)],4),([(c,1)],5)]> joinable by a reduction of rules <[([(a,1)],5),([],2),([],8)], [([],8),([(c,1)],4),([(c,1)],7)]> joinable by a reduction of rules <[([(a,1)],5),([],2),([],8)], [([],8),([(c,1)],4),([(c,1)],5)]> Critical Pair by Rules <6, 2> preceded by [(a,1)] joinable by a reduction of rules <[([],0),([],6)], [([(b,1)],7)]> joinable by a reduction of rules <[([],0),([],6)], [([(b,1)],5)]> Critical Pair by Rules <4, 3> preceded by [(b,1)] joinable by a reduction of rules <[([(b,1)],1)], [([],4)]> Critical Pair by Rules <6, 3> preceded by [(b,1)] joinable by a reduction of rules <[([],8)], [([(c,1)],7)]> joinable by a reduction of rules <[([],8)], [([(c,1)],5)]> Critical Pair by Rules <1, 4> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],0)], [([],7)]> joinable by a reduction of rules <[([(c,1)],0)], [([],5)]> Critical Pair by Rules <3, 4> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],4),([(c,1)],7)], [([],7)]> joinable by a reduction of rules <[([(c,1)],4),([(c,1)],7)], [([],5)]> joinable by a reduction of rules <[([(c,1)],4),([(c,1)],5)], [([],7)]> joinable by a reduction of rules <[([(c,1)],4),([(c,1)],5)], [([],5)]> joinable by a reduction of rules <[], [([(b,1)],2),([],8)]> Critical Pair by Rules <5, 4> preceded by [(c,1)] joinable by a reduction of rules <[], [([],7),([(c,1)],6),([],4),([],7)]> joinable by a reduction of rules <[], [([],7),([(c,1)],6),([],4),([],5)]> joinable by a reduction of rules <[], [([],5),([(c,1)],6),([],4),([],7)]> joinable by a reduction of rules <[], [([],5),([(c,1)],6),([],4),([],5)]> joinable by a reduction of rules <[], [([],1),([(a,1)],7),([],2),([],8)]> joinable by a reduction of rules <[], [([],1),([(a,1)],5),([],2),([],8)]> Critical Pair by Rules <7, 4> preceded by [(c,1)] joinable by a reduction of rules <[], [([],7),([(c,1)],6),([],4),([],7)]> joinable by a reduction of rules <[], [([],7),([(c,1)],6),([],4),([],5)]> joinable by a reduction of rules <[], [([],5),([(c,1)],6),([],4),([],7)]> joinable by a reduction of rules <[], [([],5),([(c,1)],6),([],4),([],5)]> joinable by a reduction of rules <[], [([],1),([(a,1)],7),([],2),([],8)]> joinable by a reduction of rules <[], [([],1),([(a,1)],5),([],2),([],8)]> Critical Pair by Rules <8, 4> preceded by [(c,1)] joinable by a reduction of rules <[], [([(b,1)],0),([(b,1)],6),([],8)]> joinable by a reduction of rules <[], [([(b,1)],0),([],3),([(c,1)],7)]> joinable by a reduction of rules <[], [([(b,1)],0),([],3),([(c,1)],5)]> joinable by a reduction of rules <[], [([],7),([(c,1)],4),([(c,1)],7)]> joinable by a reduction of rules <[], [([],7),([(c,1)],4),([(c,1)],5)]> joinable by a reduction of rules <[], [([],5),([(c,1)],4),([(c,1)],7)]> joinable by a reduction of rules <[], [([],5),([(c,1)],4),([(c,1)],5)]> Critical Pair by Rules <0, 5> preceded by [(b,1)] joinable by a reduction of rules <[([],3)], [([(c,1)],4)]> Critical Pair by Rules <2, 5> preceded by [(b,1)] joinable by a reduction of rules <[([],8),([(c,1)],4),([(c,1)],7)], []> joinable by a reduction of rules <[([],8),([(c,1)],4),([(c,1)],5)], []> Critical Pair by Rules <0, 6> preceded by [(c,1)] joinable by a reduction of rules <[], [([(b,1)],4),([],8)]> Critical Pair by Rules <2, 6> preceded by [(c,1)] joinable by a reduction of rules <[([],4),([],7)], [([],3),([(c,1)],3)]> joinable by a reduction of rules <[([],4),([],5)], [([],3),([(c,1)],3)]> Critical Pair by Rules <0, 7> preceded by [(b,1)] joinable by a reduction of rules <[([],3)], [([(c,1)],4)]> Critical Pair by Rules <2, 7> preceded by [(b,1)] joinable by a reduction of rules <[([],8),([(c,1)],4),([(c,1)],7)], []> joinable by a reduction of rules <[([],8),([(c,1)],4),([(c,1)],5)], []> Critical Pair by Rules <1, 8> preceded by [(b,1)] joinable by a reduction of rules <[([],7)], [([(c,1)],6),([(c,1)],3)]> joinable by a reduction of rules <[([],5)], [([(c,1)],6),([(c,1)],3)]> Critical Pair by Rules <3, 8> preceded by [(b,1)] joinable by a reduction of rules <[([],3),([(c,1)],8)], []> Critical Pair by Rules <5, 8> preceded by [(b,1)] joinable by a reduction of rules <[([],3)], [([(c,1)],6)]> Critical Pair by Rules <7, 8> preceded by [(b,1)] joinable by a reduction of rules <[([],3)], [([(c,1)],6)]> Critical Pair by Rules <8, 8> preceded by [(b,1)] joinable by a reduction of rules <[([],3),([(c,1)],3)], []> Critical Pair by Rules <5, 1> preceded by [] joinable by a reduction of rules <[], [([],0),([],6),([],3),([],4),([],7)]> joinable by a reduction of rules <[], [([],0),([],6),([],3),([],4),([],5)]> Critical Pair by Rules <7, 1> preceded by [] joinable by a reduction of rules <[], [([],0),([],6),([],3),([],4),([],7)]> joinable by a reduction of rules <[], [([],0),([],6),([],3),([],4),([],5)]> Critical Pair by Rules <7, 5> preceded by [] joinable by a reduction of rules <[], []> unknown Diagram Decreasing check Non-Confluence... obtain 15 rules by 3 steps unfolding obtain 100 candidates for checking non-joinability check by TCAP-Approximation (failure) check by Ordering(rpo), check by Tree-Automata Approximation (failure) check by Interpretation(mod2) (failure) check by Descendants-Approximation, check by Ordering(poly) (failure) unknown Non-Confluence unknown Huet (modulo AC) check by Reduction-Preserving Completion... failure(empty P) unknown Reduction-Preserving Completion check by Ordered Rewriting... remove redundants rules and split R-part: [ a(b(?x)) -> c(a(?x)), b(a(?x)) -> a(b(?x)), a(c(?x)) -> b(b(?x)), b(c(?x)) -> c(b(?x)), c(b(?x)) -> b(a(?x)), b(a(?x)) -> c(c(?x)), c(a(?x)) -> b(c(?x)), b(a(?x)) -> c(c(?x)), b(b(?x)) -> c(c(?x)) ] E-part: [ ] ...failed to find a suitable LPO. unknown Confluence by Ordered Rewriting Direct Methods: Can't judge Try Persistent Decomposition for... [ a(b(?x)) -> c(a(?x)), b(a(?x)) -> a(b(?x)), a(c(?x)) -> b(b(?x)), b(c(?x)) -> c(b(?x)), c(b(?x)) -> b(a(?x)), b(a(?x)) -> c(c(?x)), c(a(?x)) -> b(c(?x)), b(a(?x)) -> c(c(?x)), b(b(?x)) -> c(c(?x)) ] Sort Assignment: a : 16=>16 b : 16=>16 c : 16=>16 maximal types: {16} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ a(b(?x)) -> c(a(?x)), b(a(?x)) -> a(b(?x)), a(c(?x)) -> b(b(?x)), b(c(?x)) -> c(b(?x)), c(b(?x)) -> b(a(?x)), b(a(?x)) -> c(c(?x)), c(a(?x)) -> b(c(?x)), b(a(?x)) -> c(c(?x)), b(b(?x)) -> c(c(?x)) ] Layer Preserving Decomposition failed: Can't judge Try Commutative Decomposition for... [ a(b(?x)) -> c(a(?x)), b(a(?x)) -> a(b(?x)), a(c(?x)) -> b(b(?x)), b(c(?x)) -> c(b(?x)), c(b(?x)) -> b(a(?x)), b(a(?x)) -> c(c(?x)), c(a(?x)) -> b(c(?x)), b(a(?x)) -> c(c(?x)), b(b(?x)) -> c(c(?x)) ] Outside Critical Pair: by Rules <5, 1> develop reducts from lhs term... <{}, c(c(?x_5))> develop reducts from rhs term... <{0}, c(a(?x_5))> <{}, a(b(?x_5))> Outside Critical Pair: by Rules <7, 1> develop reducts from lhs term... <{}, c(c(?x_7))> develop reducts from rhs term... <{0}, c(a(?x_7))> <{}, a(b(?x_7))> Outside Critical Pair: by Rules <7, 5> develop reducts from lhs term... <{}, c(c(?x_7))> develop reducts from rhs term... <{}, c(c(?x_7))> Inside Critical Pair: by Rules <1, 0> develop reducts from lhs term... <{0}, a(c(a(?x_1)))> <{}, a(a(b(?x_1)))> develop reducts from rhs term... <{6}, b(c(a(?x_1)))> <{}, c(a(a(?x_1)))> Inside Critical Pair: by Rules <3, 0> develop reducts from lhs term... <{2}, b(b(b(?x_3)))> <{4}, a(b(a(?x_3)))> <{}, a(c(b(?x_3)))> develop reducts from rhs term... <{6}, b(c(c(?x_3)))> <{2}, c(b(b(?x_3)))> <{}, c(a(c(?x_3)))> Inside Critical Pair: by Rules <5, 0> develop reducts from lhs term... <{2}, b(b(c(?x_5)))> <{}, a(c(c(?x_5)))> develop reducts from rhs term... <{6}, b(c(a(?x_5)))> <{}, c(a(a(?x_5)))> Inside Critical Pair: by Rules <7, 0> develop reducts from lhs term... <{2}, b(b(c(?x_7)))> <{}, a(c(c(?x_7)))> develop reducts from rhs term... <{6}, b(c(a(?x_7)))> <{}, c(a(a(?x_7)))> Inside Critical Pair: by Rules <8, 0> develop reducts from lhs term... <{2}, b(b(c(?x_8)))> <{}, a(c(c(?x_8)))> develop reducts from rhs term... <{6}, b(c(b(?x_8)))> <{0}, c(c(a(?x_8)))> <{}, c(a(b(?x_8)))> Inside Critical Pair: by Rules <0, 1> develop reducts from lhs term... <{3}, c(b(a(?x)))> <{6}, b(b(c(?x)))> <{}, b(c(a(?x)))> develop reducts from rhs term... <{0}, c(a(b(?x)))> <{8}, a(c(c(?x)))> <{}, a(b(b(?x)))> Inside Critical Pair: by Rules <2, 1> develop reducts from lhs term... <{8}, c(c(b(?x_2)))> <{8}, b(c(c(?x_2)))> <{}, b(b(b(?x_2)))> develop reducts from rhs term... <{0}, c(a(c(?x_2)))> <{3}, a(c(b(?x_2)))> <{}, a(b(c(?x_2)))> Inside Critical Pair: by Rules <4, 2> develop reducts from lhs term... <{0}, c(a(a(?x_4)))> <{7}, a(c(c(?x_4)))> <{5}, a(c(c(?x_4)))> <{1}, a(a(b(?x_4)))> <{}, a(b(a(?x_4)))> develop reducts from rhs term... <{8}, c(c(b(?x_4)))> <{8}, b(c(c(?x_4)))> <{}, b(b(b(?x_4)))> Inside Critical Pair: by Rules <6, 2> develop reducts from lhs term... <{0}, c(a(c(?x_6)))> <{3}, a(c(b(?x_6)))> <{}, a(b(c(?x_6)))> develop reducts from rhs term... <{8}, c(c(a(?x_6)))> <{7}, b(c(c(?x_6)))> <{5}, b(c(c(?x_6)))> <{1}, b(a(b(?x_6)))> <{}, b(b(a(?x_6)))> Inside Critical Pair: by Rules <4, 3> develop reducts from lhs term... <{8}, c(c(a(?x_4)))> <{7}, b(c(c(?x_4)))> <{5}, b(c(c(?x_4)))> <{1}, b(a(b(?x_4)))> <{}, b(b(a(?x_4)))> develop reducts from rhs term... <{4}, b(a(b(?x_4)))> <{8}, c(c(c(?x_4)))> <{}, c(b(b(?x_4)))> Inside Critical Pair: by Rules <6, 3> develop reducts from lhs term... <{8}, c(c(c(?x_6)))> <{3}, b(c(b(?x_6)))> <{}, b(b(c(?x_6)))> develop reducts from rhs term... <{4}, b(a(a(?x_6)))> <{7}, c(c(c(?x_6)))> <{5}, c(c(c(?x_6)))> <{1}, c(a(b(?x_6)))> <{}, c(b(a(?x_6)))> Inside Critical Pair: by Rules <1, 4> develop reducts from lhs term... <{6}, b(c(b(?x_1)))> <{0}, c(c(a(?x_1)))> <{}, c(a(b(?x_1)))> develop reducts from rhs term... <{7}, c(c(a(?x_1)))> <{5}, c(c(a(?x_1)))> <{1}, a(b(a(?x_1)))> <{}, b(a(a(?x_1)))> Inside Critical Pair: by Rules <3, 4> develop reducts from lhs term... <{4}, c(b(a(?x_3)))> <{}, c(c(b(?x_3)))> develop reducts from rhs term... <{7}, c(c(c(?x_3)))> <{5}, c(c(c(?x_3)))> <{1}, a(b(c(?x_3)))> <{2}, b(b(b(?x_3)))> <{}, b(a(c(?x_3)))> Inside Critical Pair: by Rules <5, 4> develop reducts from lhs term... <{}, c(c(c(?x_5)))> develop reducts from rhs term... <{7}, c(c(a(?x_5)))> <{5}, c(c(a(?x_5)))> <{1}, a(b(a(?x_5)))> <{}, b(a(a(?x_5)))> Inside Critical Pair: by Rules <7, 4> develop reducts from lhs term... <{}, c(c(c(?x_7)))> develop reducts from rhs term... <{7}, c(c(a(?x_7)))> <{5}, c(c(a(?x_7)))> <{1}, a(b(a(?x_7)))> <{}, b(a(a(?x_7)))> Inside Critical Pair: by Rules <8, 4> develop reducts from lhs term... <{}, c(c(c(?x_8)))> develop reducts from rhs term... <{7}, c(c(b(?x_8)))> <{5}, c(c(b(?x_8)))> <{1}, a(b(b(?x_8)))> <{0}, b(c(a(?x_8)))> <{}, b(a(b(?x_8)))> Inside Critical Pair: by Rules <0, 5> develop reducts from lhs term... <{3}, c(b(a(?x)))> <{6}, b(b(c(?x)))> <{}, b(c(a(?x)))> develop reducts from rhs term... <{4}, c(b(a(?x)))> <{}, c(c(b(?x)))> Inside Critical Pair: by Rules <2, 5> develop reducts from lhs term... <{8}, c(c(b(?x_2)))> <{8}, b(c(c(?x_2)))> <{}, b(b(b(?x_2)))> develop reducts from rhs term... <{}, c(c(c(?x_2)))> Inside Critical Pair: by Rules <0, 6> develop reducts from lhs term... <{6}, c(b(c(?x)))> <{}, c(c(a(?x)))> develop reducts from rhs term... <{3}, c(b(b(?x)))> <{4}, b(b(a(?x)))> <{}, b(c(b(?x)))> Inside Critical Pair: by Rules <2, 6> develop reducts from lhs term... <{4}, b(a(b(?x_2)))> <{8}, c(c(c(?x_2)))> <{}, c(b(b(?x_2)))> develop reducts from rhs term... <{3}, c(b(c(?x_2)))> <{}, b(c(c(?x_2)))> Inside Critical Pair: by Rules <0, 7> develop reducts from lhs term... <{3}, c(b(a(?x)))> <{6}, b(b(c(?x)))> <{}, b(c(a(?x)))> develop reducts from rhs term... <{4}, c(b(a(?x)))> <{}, c(c(b(?x)))> Inside Critical Pair: by Rules <2, 7> develop reducts from lhs term... <{8}, c(c(b(?x_2)))> <{8}, b(c(c(?x_2)))> <{}, b(b(b(?x_2)))> develop reducts from rhs term... <{}, c(c(c(?x_2)))> Inside Critical Pair: by Rules <1, 8> develop reducts from lhs term... <{7}, c(c(b(?x_1)))> <{5}, c(c(b(?x_1)))> <{1}, a(b(b(?x_1)))> <{0}, b(c(a(?x_1)))> <{}, b(a(b(?x_1)))> develop reducts from rhs term... <{6}, c(b(c(?x_1)))> <{}, c(c(a(?x_1)))> Inside Critical Pair: by Rules <3, 8> develop reducts from lhs term... <{3}, c(b(b(?x_3)))> <{4}, b(b(a(?x_3)))> <{}, b(c(b(?x_3)))> develop reducts from rhs term... <{}, c(c(c(?x_3)))> Inside Critical Pair: by Rules <5, 8> develop reducts from lhs term... <{3}, c(b(c(?x_5)))> <{}, b(c(c(?x_5)))> develop reducts from rhs term... <{6}, c(b(c(?x_5)))> <{}, c(c(a(?x_5)))> Inside Critical Pair: by Rules <7, 8> develop reducts from lhs term... <{3}, c(b(c(?x_7)))> <{}, b(c(c(?x_7)))> develop reducts from rhs term... <{6}, c(b(c(?x_7)))> <{}, c(c(a(?x_7)))> Commutative Decomposition failed: Can't judge No further decomposition possible Combined result: Can't judge 1029.trs: Failure(unknown CR) (3240 msec.)