MAYBE (ignored inputs)COMMENT reduction failed Rewrite Rules: [ c(a(?x)) -> a(b(?x)), c(b(?x)) -> b(b(?x)), b(b(?x)) -> a(a(?x)), a(a(?x)) -> b(a(?x)), c(c(?x)) -> a(a(?x)), a(b(?x)) -> c(c(?x)), a(b(?x)) -> b(a(?x)), b(c(?x)) -> c(c(?x)), c(a(?x)) -> a(a(?x)) ] Apply Direct Methods... Inner CPs: [ c(b(a(?x_3))) = a(b(a(?x_3))), c(c(c(?x_5))) = a(b(b(?x_5))), c(b(a(?x_6))) = a(b(b(?x_6))), c(a(a(?x_2))) = b(b(b(?x_2))), c(c(c(?x_7))) = b(b(c(?x_7))), b(c(c(?x_7))) = a(a(c(?x_7))), a(c(c(?x_5))) = b(a(b(?x_5))), a(b(a(?x_6))) = b(a(b(?x_6))), c(a(b(?x))) = a(a(a(?x))), c(b(b(?x_1))) = a(a(b(?x_1))), c(a(a(?x_8))) = a(a(a(?x_8))), a(a(a(?x_2))) = c(c(b(?x_2))), a(c(c(?x_7))) = c(c(c(?x_7))), a(a(a(?x_2))) = b(a(b(?x_2))), a(c(c(?x_7))) = b(a(c(?x_7))), b(a(b(?x))) = c(c(a(?x))), b(b(b(?x_1))) = c(c(b(?x_1))), b(a(a(?x_4))) = c(c(c(?x_4))), b(a(a(?x_8))) = c(c(a(?x_8))), c(b(a(?x_3))) = a(a(a(?x_3))), c(c(c(?x_5))) = a(a(b(?x_5))), c(b(a(?x_6))) = a(a(b(?x_6))), b(a(a(?x))) = a(a(b(?x))), a(b(a(?x))) = b(a(a(?x))), c(a(a(?x))) = a(a(c(?x))) ] Outer CPs: [ a(b(?x)) = a(a(?x)), c(c(?x_5)) = b(a(?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(?x)) = a(b(?x)), c(b(a(?x_4))) = a(b(a(?x_4))), c(c(c(?x_6))) = a(b(b(?x_6))), c(b(a(?x_7))) = a(b(b(?x_7))), a(a(b(a(?x_4)))) = c(a(b(a(?x_4)))), a(a(c(c(?x_6)))) = c(a(b(b(?x_6)))), a(a(b(a(?x_7)))) = c(a(b(b(?x_7)))), c(c(b(a(?x_4)))) = b(a(b(a(?x_4)))), c(c(c(c(?x_6)))) = b(a(b(b(?x_6)))), c(c(b(a(?x_7)))) = b(a(b(b(?x_7)))), a(a(a(?x))) = c(a(b(?x))), c(c(a(?x))) = b(a(b(?x))), c(a(a(?x_3))) = b(b(b(?x_3))), c(c(c(?x_8))) = b(b(c(?x_8))), a(a(a(a(?x_3)))) = c(b(b(b(?x_3)))), a(a(c(c(?x_8)))) = c(b(b(c(?x_8)))), c(c(a(a(?x_3)))) = b(b(b(b(?x_3)))), c(c(c(c(?x_8)))) = b(b(b(c(?x_8)))), a(a(b(?x))) = c(b(b(?x))), c(c(b(?x))) = b(b(b(?x))), b(a(a(?x_1))) = a(a(b(?x_1))), b(c(c(?x_8))) = a(a(c(?x_8))), a(a(a(a(?x_1)))) = b(a(a(b(?x_1)))), a(a(c(c(?x_8)))) = b(a(a(c(?x_8)))), b(b(a(a(?x_1)))) = c(a(a(b(?x_1)))), b(b(c(c(?x_8)))) = c(a(a(c(?x_8)))), c(c(a(a(?x_1)))) = a(a(a(b(?x_1)))), c(c(c(c(?x_8)))) = a(a(a(c(?x_8)))), b(a(a(a(?x_1)))) = a(a(a(b(?x_1)))), b(a(c(c(?x_8)))) = a(a(a(c(?x_8)))), a(a(b(?x))) = b(a(a(?x))), b(b(b(?x))) = c(a(a(?x))), c(c(b(?x))) = a(a(a(?x))), b(a(b(?x))) = a(a(a(?x))), a(b(a(?x_1))) = b(a(a(?x_1))), a(c(c(?x_6))) = b(a(b(?x_6))), a(b(a(?x_7))) = b(a(b(?x_7))), b(a(b(a(?x_1)))) = a(b(a(a(?x_1)))), b(a(c(c(?x_6)))) = a(b(a(b(?x_6)))), b(a(b(a(?x_7)))) = a(b(a(b(?x_7)))), a(b(b(a(?x_1)))) = c(b(a(a(?x_1)))), a(b(c(c(?x_6)))) = c(b(a(b(?x_6)))), a(b(b(a(?x_7)))) = c(b(a(b(?x_7)))), a(a(b(a(?x_1)))) = c(b(a(a(?x_1)))), a(a(c(c(?x_6)))) = c(b(a(b(?x_6)))), a(a(b(a(?x_7)))) = c(b(a(b(?x_7)))), b(a(a(?x))) = a(b(a(?x))), a(b(a(?x))) = c(b(a(?x))), a(a(a(?x))) = c(b(a(?x))), c(a(a(?x_1))) = a(a(c(?x_1))), c(a(b(?x_2))) = a(a(a(?x_2))), c(b(b(?x_3))) = a(a(b(?x_3))), c(a(a(?x_9))) = a(a(a(?x_9))), a(a(a(a(?x_1)))) = c(a(a(c(?x_1)))), a(a(a(b(?x_2)))) = c(a(a(a(?x_2)))), a(a(b(b(?x_3)))) = c(a(a(b(?x_3)))), a(a(a(a(?x_9)))) = c(a(a(a(?x_9)))), c(c(a(a(?x_1)))) = b(a(a(c(?x_1)))), c(c(a(b(?x_2)))) = b(a(a(a(?x_2)))), c(c(b(b(?x_3)))) = b(a(a(b(?x_3)))), c(c(a(a(?x_9)))) = b(a(a(a(?x_9)))), a(a(c(?x))) = c(a(a(?x))), c(c(c(?x))) = b(a(a(?x))), b(a(?x)) = c(c(?x)), a(a(a(?x_4))) = c(c(b(?x_4))), a(c(c(?x_8))) = c(c(c(?x_8))), a(b(a(a(?x_4)))) = c(c(c(b(?x_4)))), a(b(c(c(?x_8)))) = c(c(c(c(?x_8)))), b(a(a(a(?x_4)))) = a(c(c(b(?x_4)))), b(a(c(c(?x_8)))) = a(c(c(c(?x_8)))), a(a(a(a(?x_4)))) = c(c(c(b(?x_4)))), a(a(c(c(?x_8)))) = c(c(c(c(?x_8)))), a(b(b(?x))) = c(c(c(?x))), b(a(b(?x))) = a(c(c(?x))), a(a(b(?x))) = c(c(c(?x))), c(c(?x)) = b(a(?x)), a(a(a(?x_4))) = b(a(b(?x_4))), a(c(c(?x_8))) = b(a(c(?x_8))), a(b(a(a(?x_4)))) = c(b(a(b(?x_4)))), a(b(c(c(?x_8)))) = c(b(a(c(?x_8)))), b(a(a(a(?x_4)))) = a(b(a(b(?x_4)))), b(a(c(c(?x_8)))) = a(b(a(c(?x_8)))), a(a(a(a(?x_4)))) = c(b(a(b(?x_4)))), a(a(c(c(?x_8)))) = c(b(a(c(?x_8)))), a(b(b(?x))) = c(b(a(?x))), b(a(b(?x))) = a(b(a(?x))), a(a(b(?x))) = c(b(a(?x))), b(a(b(?x_2))) = c(c(a(?x_2))), b(b(b(?x_3))) = c(c(b(?x_3))), b(a(a(?x_6))) = c(c(c(?x_6))), b(a(a(?x_9))) = c(c(a(?x_9))), b(b(a(b(?x_2)))) = c(c(c(a(?x_2)))), b(b(b(b(?x_3)))) = c(c(c(b(?x_3)))), b(b(a(a(?x_6)))) = c(c(c(c(?x_6)))), b(b(a(a(?x_9)))) = c(c(c(a(?x_9)))), a(a(a(b(?x_2)))) = b(c(c(a(?x_2)))), a(a(b(b(?x_3)))) = b(c(c(b(?x_3)))), a(a(a(a(?x_6)))) = b(c(c(c(?x_6)))), a(a(a(a(?x_9)))) = b(c(c(a(?x_9)))), c(c(a(b(?x_2)))) = a(c(c(a(?x_2)))), c(c(b(b(?x_3)))) = a(c(c(b(?x_3)))), c(c(a(a(?x_6)))) = a(c(c(c(?x_6)))), c(c(a(a(?x_9)))) = a(c(c(a(?x_9)))), b(a(a(b(?x_2)))) = a(c(c(a(?x_2)))), b(a(b(b(?x_3)))) = a(c(c(b(?x_3)))), b(a(a(a(?x_6)))) = a(c(c(c(?x_6)))), b(a(a(a(?x_9)))) = a(c(c(a(?x_9)))), b(b(c(?x))) = c(c(c(?x))), a(a(c(?x))) = b(c(c(?x))), c(c(c(?x))) = a(c(c(?x))), b(a(c(?x))) = a(c(c(?x))), a(b(?x)) = a(a(?x)), c(b(a(?x_5))) = a(a(a(?x_5))), c(c(c(?x_7))) = a(a(b(?x_7))), c(b(a(?x_8))) = a(a(b(?x_8))), a(a(b(a(?x_5)))) = c(a(a(a(?x_5)))), a(a(c(c(?x_7)))) = c(a(a(b(?x_7)))), a(a(b(a(?x_8)))) = c(a(a(b(?x_8)))), c(c(b(a(?x_5)))) = b(a(a(a(?x_5)))), c(c(c(c(?x_7)))) = b(a(a(b(?x_7)))), c(c(b(a(?x_8)))) = b(a(a(b(?x_8)))), a(a(a(?x))) = c(a(a(?x))), c(c(a(?x))) = b(a(a(?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 <3, 0> preceded by [(c,1)] joinable by a reduction of rules <[([],1)], [([],6),([(b,1)],3)]> joinable by a reduction of rules <[([],1),([],2)], [([],5),([],4)]> Critical Pair by Rules <5, 0> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],4),([],8)], [([(a,1)],2)]> joinable by a reduction of rules <[([(c,1)],4),([],0)], [([(a,1)],2),([(a,1)],3)]> Critical Pair by Rules <6, 0> preceded by [(c,1)] joinable by a reduction of rules <[([],1),([],2)], [([(a,1)],2)]> joinable by a reduction of rules <[([],1)], [([],6),([(b,1)],6)]> Critical Pair by Rules <2, 1> preceded by [(c,1)] joinable by a reduction of rules <[([],8),([],3)], [([(b,1)],2)]> joinable by a reduction of rules <[([],0),([],6)], [([(b,1)],2)]> joinable by a reduction of rules <[([],0)], [([],2),([(a,1)],6)]> joinable by a reduction of rules <[([(c,1)],3),([],1)], [([(b,1)],2),([(b,1)],3)]> joinable by a reduction of rules <[([],8),([(a,1)],3)], [([],2),([(a,1)],6)]> Critical Pair by Rules <7, 1> preceded by [(c,1)] joinable by a reduction of rules <[([],4)], [([],2)]> Critical Pair by Rules <7, 2> preceded by [(b,1)] joinable by a reduction of rules <[([],7),([],4)], []> Critical Pair by Rules <5, 3> preceded by [(a,1)] joinable by a reduction of rules <[([(a,1)],4)], [([(b,1)],6),([],2)]> joinable by a reduction of rules <[([(a,1)],4),([],3)], [([(b,1)],5),([(b,1)],4)]> Critical Pair by Rules <6, 3> preceded by [(a,1)] joinable by a reduction of rules <[([],6),([(b,1)],3)], [([(b,1)],6)]> joinable by a reduction of rules <[([],6)], [([(b,1)],5),([(b,1)],4)]> joinable by a reduction of rules <[([],5),([],4)], [([(b,1)],6),([],2)]> Critical Pair by Rules <0, 4> preceded by [(c,1)] joinable by a reduction of rules <[([],8),([(a,1)],6)], [([(a,1)],3)]> joinable by a reduction of rules <[([],0),([(a,1)],2)], []> joinable by a reduction of rules <[([(c,1)],6),([],1)], [([],3),([(b,1)],3)]> Critical Pair by Rules <1, 4> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],2),([],0)], [([(a,1)],6)]> joinable by a reduction of rules <[([],1),([],2)], []> joinable by a reduction of rules <[([(c,1)],2),([],8)], [([(a,1)],5),([(a,1)],4)]> joinable by a reduction of rules <[([],1),([(b,1)],2)], [([(a,1)],6),([],6)]> Critical Pair by Rules <8, 4> preceded by [(c,1)] joinable by a reduction of rules <[([],8)], []> joinable by a reduction of rules <[([],0)], [([(a,1)],3)]> Critical Pair by Rules <2, 5> preceded by [(a,1)] joinable by a reduction of rules <[([(a,1)],3)], [([],4),([(a,1)],6)]> Critical Pair by Rules <7, 5> preceded by [(a,1)] joinable by a reduction of rules <[([(a,1)],4)], [([(c,1)],4),([],8)]> joinable by a reduction of rules <[([(a,1)],4),([(a,1)],3)], [([(c,1)],4),([],0)]> Critical Pair by Rules <2, 6> preceded by [(a,1)] joinable by a reduction of rules <[([],3),([(b,1)],3)], [([(b,1)],6)]> joinable by a reduction of rules <[], [([(b,1)],6),([],2)]> joinable by a reduction of rules <[([],3)], [([(b,1)],5),([(b,1)],4)]> joinable by a reduction of rules <[([(a,1)],3),([],6)], [([(b,1)],5),([(b,1)],4)]> Critical Pair by Rules <7, 6> preceded by [(a,1)] unknown Diagram Decreasing check Non-Confluence... obtain 13 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: [ c(a(?x)) -> a(b(?x)), c(b(?x)) -> b(b(?x)), b(b(?x)) -> a(a(?x)), a(a(?x)) -> b(a(?x)), c(c(?x)) -> a(a(?x)), a(b(?x)) -> c(c(?x)), a(b(?x)) -> b(a(?x)), b(c(?x)) -> c(c(?x)), c(a(?x)) -> a(a(?x)) ] E-part: [ ] ...failed to find a suitable LPO. unknown Confluence by Ordered Rewriting Direct Methods: Can't judge Try Persistent Decomposition for... [ c(a(?x)) -> a(b(?x)), c(b(?x)) -> b(b(?x)), b(b(?x)) -> a(a(?x)), a(a(?x)) -> b(a(?x)), c(c(?x)) -> a(a(?x)), a(b(?x)) -> c(c(?x)), a(b(?x)) -> b(a(?x)), b(c(?x)) -> c(c(?x)), c(a(?x)) -> a(a(?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... [ c(a(?x)) -> a(b(?x)), c(b(?x)) -> b(b(?x)), b(b(?x)) -> a(a(?x)), a(a(?x)) -> b(a(?x)), c(c(?x)) -> a(a(?x)), a(b(?x)) -> c(c(?x)), a(b(?x)) -> b(a(?x)), b(c(?x)) -> c(c(?x)), c(a(?x)) -> a(a(?x)) ] Layer Preserving Decomposition failed: Can't judge Try Commutative Decomposition for... [ c(a(?x)) -> a(b(?x)), c(b(?x)) -> b(b(?x)), b(b(?x)) -> a(a(?x)), a(a(?x)) -> b(a(?x)), c(c(?x)) -> a(a(?x)), a(b(?x)) -> c(c(?x)), a(b(?x)) -> b(a(?x)), b(c(?x)) -> c(c(?x)), c(a(?x)) -> a(a(?x)) ] Outside Critical Pair: by Rules <8, 0> develop reducts from lhs term... <{3}, b(a(?x_8))> <{}, a(a(?x_8))> develop reducts from rhs term... <{6}, b(a(?x_8))> <{5}, c(c(?x_8))> <{}, a(b(?x_8))> Outside Critical Pair: by Rules <6, 5> develop reducts from lhs term... <{}, b(a(?x_6))> develop reducts from rhs term... <{4}, a(a(?x_6))> <{}, c(c(?x_6))> Inside Critical Pair: by Rules <3, 0> develop reducts from lhs term... <{1}, b(b(a(?x_3)))> <{}, c(b(a(?x_3)))> develop reducts from rhs term... <{6}, b(a(a(?x_3)))> <{5}, c(c(a(?x_3)))> <{}, a(b(a(?x_3)))> Inside Critical Pair: by Rules <5, 0> develop reducts from lhs term... <{4}, a(a(c(?x_5)))> <{4}, c(a(a(?x_5)))> <{}, c(c(c(?x_5)))> develop reducts from rhs term... <{6}, b(a(b(?x_5)))> <{5}, c(c(b(?x_5)))> <{2}, a(a(a(?x_5)))> <{}, a(b(b(?x_5)))> Inside Critical Pair: by Rules <6, 0> develop reducts from lhs term... <{1}, b(b(a(?x_6)))> <{}, c(b(a(?x_6)))> develop reducts from rhs term... <{6}, b(a(b(?x_6)))> <{5}, c(c(b(?x_6)))> <{2}, a(a(a(?x_6)))> <{}, a(b(b(?x_6)))> Inside Critical Pair: by Rules <2, 1> develop reducts from lhs term... <{8}, a(a(a(?x_2)))> <{0}, a(b(a(?x_2)))> <{3}, c(b(a(?x_2)))> <{}, c(a(a(?x_2)))> develop reducts from rhs term... <{2}, a(a(b(?x_2)))> <{2}, b(a(a(?x_2)))> <{}, b(b(b(?x_2)))> Inside Critical Pair: by Rules <7, 1> develop reducts from lhs term... <{4}, a(a(c(?x_7)))> <{4}, c(a(a(?x_7)))> <{}, c(c(c(?x_7)))> develop reducts from rhs term... <{2}, a(a(c(?x_7)))> <{7}, b(c(c(?x_7)))> <{}, b(b(c(?x_7)))> Inside Critical Pair: by Rules <7, 2> develop reducts from lhs term... <{7}, c(c(c(?x_7)))> <{4}, b(a(a(?x_7)))> <{}, b(c(c(?x_7)))> develop reducts from rhs term... <{3}, b(a(c(?x_7)))> <{}, a(a(c(?x_7)))> Inside Critical Pair: by Rules <5, 3> develop reducts from lhs term... <{4}, a(a(a(?x_5)))> <{}, a(c(c(?x_5)))> develop reducts from rhs term... <{6}, b(b(a(?x_5)))> <{5}, b(c(c(?x_5)))> <{}, b(a(b(?x_5)))> Inside Critical Pair: by Rules <6, 3> develop reducts from lhs term... <{6}, b(a(a(?x_6)))> <{5}, c(c(a(?x_6)))> <{}, a(b(a(?x_6)))> develop reducts from rhs term... <{6}, b(b(a(?x_6)))> <{5}, b(c(c(?x_6)))> <{}, b(a(b(?x_6)))> Inside Critical Pair: by Rules <0, 4> develop reducts from lhs term... <{8}, a(a(b(?x)))> <{0}, a(b(b(?x)))> <{6}, c(b(a(?x)))> <{5}, c(c(c(?x)))> <{}, c(a(b(?x)))> develop reducts from rhs term... <{3}, b(a(a(?x)))> <{3}, a(b(a(?x)))> <{}, a(a(a(?x)))> Inside Critical Pair: by Rules <1, 4> develop reducts from lhs term... <{1}, b(b(b(?x_1)))> <{2}, c(a(a(?x_1)))> <{}, c(b(b(?x_1)))> develop reducts from rhs term... <{3}, b(a(b(?x_1)))> <{6}, a(b(a(?x_1)))> <{5}, a(c(c(?x_1)))> <{}, a(a(b(?x_1)))> Inside Critical Pair: by Rules <8, 4> develop reducts from lhs term... <{8}, a(a(a(?x_8)))> <{0}, a(b(a(?x_8)))> <{3}, c(b(a(?x_8)))> <{}, c(a(a(?x_8)))> develop reducts from rhs term... <{3}, b(a(a(?x_8)))> <{3}, a(b(a(?x_8)))> <{}, a(a(a(?x_8)))> Inside Critical Pair: by Rules <2, 5> develop reducts from lhs term... <{3}, b(a(a(?x_2)))> <{3}, a(b(a(?x_2)))> <{}, a(a(a(?x_2)))> develop reducts from rhs term... <{4}, a(a(b(?x_2)))> <{1}, c(b(b(?x_2)))> <{}, c(c(b(?x_2)))> Inside Critical Pair: by Rules <7, 5> develop reducts from lhs term... <{4}, a(a(a(?x_7)))> <{}, a(c(c(?x_7)))> develop reducts from rhs term... <{4}, a(a(c(?x_7)))> <{4}, c(a(a(?x_7)))> <{}, c(c(c(?x_7)))> Inside Critical Pair: by Rules <2, 6> develop reducts from lhs term... <{3}, b(a(a(?x_2)))> <{3}, a(b(a(?x_2)))> <{}, a(a(a(?x_2)))> develop reducts from rhs term... <{6}, b(b(a(?x_2)))> <{5}, b(c(c(?x_2)))> <{}, b(a(b(?x_2)))> Inside Critical Pair: by Rules <7, 6> develop reducts from lhs term... <{4}, a(a(a(?x_7)))> <{}, a(c(c(?x_7)))> develop reducts from rhs term... <{}, b(a(c(?x_7)))> Inside Critical Pair: by Rules <0, 7> develop reducts from lhs term... <{6}, b(b(a(?x)))> <{5}, b(c(c(?x)))> <{}, b(a(b(?x)))> develop reducts from rhs term... <{4}, a(a(a(?x)))> <{8}, c(a(a(?x)))> <{0}, c(a(b(?x)))> <{}, c(c(a(?x)))> Inside Critical Pair: by Rules <1, 7> develop reducts from lhs term... <{2}, a(a(b(?x_1)))> <{2}, b(a(a(?x_1)))> <{}, b(b(b(?x_1)))> develop reducts from rhs term... <{4}, a(a(b(?x_1)))> <{1}, c(b(b(?x_1)))> <{}, c(c(b(?x_1)))> Inside Critical Pair: by Rules <4, 7> develop reducts from lhs term... <{3}, b(b(a(?x_4)))> <{}, b(a(a(?x_4)))> develop reducts from rhs term... <{4}, a(a(c(?x_4)))> <{4}, c(a(a(?x_4)))> <{}, c(c(c(?x_4)))> Inside Critical Pair: by Rules <8, 7> develop reducts from lhs term... <{3}, b(b(a(?x_8)))> <{}, b(a(a(?x_8)))> develop reducts from rhs term... <{4}, a(a(a(?x_8)))> <{8}, c(a(a(?x_8)))> <{0}, c(a(b(?x_8)))> <{}, c(c(a(?x_8)))> Inside Critical Pair: by Rules <3, 8> develop reducts from lhs term... <{1}, b(b(a(?x_3)))> <{}, c(b(a(?x_3)))> develop reducts from rhs term... <{3}, b(a(a(?x_3)))> <{3}, a(b(a(?x_3)))> <{}, a(a(a(?x_3)))> Inside Critical Pair: by Rules <5, 8> develop reducts from lhs term... <{4}, a(a(c(?x_5)))> <{4}, c(a(a(?x_5)))> <{}, c(c(c(?x_5)))> develop reducts from rhs term... <{3}, b(a(b(?x_5)))> <{6}, a(b(a(?x_5)))> <{5}, a(c(c(?x_5)))> <{}, a(a(b(?x_5)))> Inside Critical Pair: by Rules <6, 8> develop reducts from lhs term... <{1}, b(b(a(?x_6)))> <{}, c(b(a(?x_6)))> develop reducts from rhs term... <{3}, b(a(b(?x_6)))> <{6}, a(b(a(?x_6)))> <{5}, a(c(c(?x_6)))> <{}, a(a(b(?x_6)))> Commutative Decomposition failed: Can't judge No further decomposition possible Combined result: Can't judge /tmp/filed2lQce.trs: Failure(unknown CR) (3351 msec.)