(ignored inputs)COMMENT submitted by: Johannes Waldmann Rewrite Rules: [ c(a(?x)) -> c(b(?x)), b(a(?x)) -> c(a(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> b(c(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> c(a(?x)), b(a(?x)) -> c(b(?x)), b(b(?x)) -> c(c(?x)) ] Apply Direct Methods... Inner CPs: [ b(c(b(?x))) = b(a(a(?x))), b(b(c(?x_3))) = b(a(b(?x_3))), b(c(a(?x_5))) = b(a(b(?x_5))), c(c(a(?x_1))) = b(c(a(?x_1))), c(b(a(?x_2))) = b(c(c(?x_2))), c(b(a(?x_4))) = b(c(c(?x_4))), c(c(b(?x_6))) = b(c(a(?x_6))), c(c(c(?x_7))) = b(c(b(?x_7))), b(c(b(?x))) = b(a(a(?x))), b(b(c(?x_3))) = b(a(b(?x_3))), b(c(a(?x_5))) = b(a(b(?x_5))), c(c(a(?x_1))) = c(a(a(?x_1))), c(b(a(?x_2))) = c(a(c(?x_2))), c(b(a(?x_4))) = c(a(c(?x_4))), c(c(b(?x_6))) = c(a(a(?x_6))), c(c(c(?x_7))) = c(a(b(?x_7))), b(c(a(?x_1))) = c(c(a(?x_1))), b(b(a(?x_2))) = c(c(c(?x_2))), b(b(a(?x_4))) = c(c(c(?x_4))), b(c(b(?x_6))) = c(c(a(?x_6))), b(c(c(?x))) = c(c(b(?x))) ] Outer CPs: [ c(a(?x_1)) = c(b(?x_1)), b(a(?x_2)) = b(a(?x_2)), b(c(?x_3)) = c(a(?x_3)) ] not Overlay, check Termination... unknown/not Terminating unknown Knuth & Bendix Linear unknown Development Closed unknown Strongly Closed unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow inner CP cond (upside-parallel) innter CP Cond (outside) unknown Upside-Parallel-Closed/Outside-Closed (inner) Parallel CPs: (not computed) unknown Toyama (Parallel CPs) Simultaneous CPs: [ b(a(a(?x))) = b(c(b(?x))), c(b(?x)) = c(a(?x)), b(c(a(?x))) = c(c(a(?x))), c(a(a(?x))) = c(c(a(?x))), c(c(a(?x))) = b(c(a(?x))), b(a(?x)) = b(a(?x)), b(c(b(?x_2))) = b(a(a(?x_2))), b(b(c(?x_4))) = b(a(b(?x_4))), b(c(a(?x_6))) = b(a(b(?x_6))), b(c(c(b(?x_2)))) = c(b(a(a(?x_2)))), b(c(b(c(?x_4)))) = c(b(a(b(?x_4)))), b(c(c(a(?x_6)))) = c(b(a(b(?x_6)))), c(a(c(b(?x_2)))) = c(b(a(a(?x_2)))), c(a(b(c(?x_4)))) = c(b(a(b(?x_4)))), c(a(c(a(?x_6)))) = c(b(a(b(?x_6)))), c(c(c(b(?x_2)))) = b(b(a(a(?x_2)))), c(c(b(c(?x_4)))) = b(b(a(b(?x_4)))), c(c(c(a(?x_6)))) = b(b(a(b(?x_6)))), b(c(c(?x))) = c(b(a(?x))), c(a(c(?x))) = c(b(a(?x))), c(c(c(?x))) = b(b(a(?x))), c(a(?x)) = b(c(?x)), c(b(a(?x_4))) = b(c(c(?x_4))), c(c(b(?x_7))) = b(c(a(?x_7))), c(c(c(?x_8))) = b(c(b(?x_8))), b(a(c(a(?x_3)))) = b(b(c(a(?x_3)))), b(a(b(a(?x_4)))) = b(b(c(c(?x_4)))), b(a(c(b(?x_7)))) = b(b(c(a(?x_7)))), b(a(c(c(?x_8)))) = b(b(c(b(?x_8)))), b(a(b(?x))) = b(b(c(?x))), b(c(?x)) = c(a(?x)), c(c(a(?x_3))) = c(a(a(?x_3))), c(b(a(?x_4))) = c(a(c(?x_4))), c(c(b(?x_7))) = c(a(a(?x_7))), c(c(c(?x_8))) = c(a(b(?x_8))), b(a(c(a(?x_3)))) = b(c(a(a(?x_3)))), b(a(b(a(?x_4)))) = b(c(a(c(?x_4)))), b(a(c(b(?x_7)))) = b(c(a(a(?x_7)))), b(a(c(c(?x_8)))) = b(c(a(b(?x_8)))), b(a(b(?x))) = b(c(a(?x))), c(a(?x)) = c(b(?x)), b(c(a(?x))) = c(c(b(?x))), c(a(a(?x))) = c(c(b(?x))), c(c(a(?x))) = b(c(b(?x))), b(c(c(?x_1))) = c(c(b(?x_1))), b(b(a(?x_4))) = c(c(c(?x_4))), b(c(b(?x_8))) = c(c(a(?x_8))), c(c(c(c(?x_1)))) = b(c(c(b(?x_1)))), c(c(c(a(?x_3)))) = b(c(c(a(?x_3)))), c(c(b(a(?x_4)))) = b(c(c(c(?x_4)))), c(c(c(b(?x_8)))) = b(c(c(a(?x_8)))), b(c(c(c(?x_1)))) = c(c(c(b(?x_1)))), b(c(c(a(?x_3)))) = c(c(c(a(?x_3)))), b(c(b(a(?x_4)))) = c(c(c(c(?x_4)))), b(c(c(b(?x_8)))) = c(c(c(a(?x_8)))), c(a(c(c(?x_1)))) = c(c(c(b(?x_1)))), c(a(c(a(?x_3)))) = c(c(c(a(?x_3)))), c(a(b(a(?x_4)))) = c(c(c(c(?x_4)))), c(a(c(b(?x_8)))) = c(c(c(a(?x_8)))), c(c(b(?x))) = b(c(c(?x))), b(c(b(?x))) = c(c(c(?x))), c(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 <0, 2> preceded by [(b,1)] joinable by a reduction of rules <[([(b,1)],5),([],4)], []> joinable by a reduction of rules <[([(b,1)],5),([],2)], []> joinable by a reduction of rules <[([(b,1)],5)], [([],6),([],3)]> Critical Pair by Rules <3, 2> preceded by [(b,1)] joinable by a reduction of rules <[([],7)], [([],6),([(c,1)],7)]> joinable by a reduction of rules <[([(b,1)],4),([(b,1)],6)], [([],6),([],3)]> joinable by a reduction of rules <[([(b,1)],2),([(b,1)],6)], [([],6),([],3)]> Critical Pair by Rules <5, 2> preceded by [(b,1)] joinable by a reduction of rules <[([(b,1)],0),([],4)], []> joinable by a reduction of rules <[([(b,1)],0),([],2)], []> joinable by a reduction of rules <[([(b,1)],0)], [([],6),([],3)]> Critical Pair by Rules <1, 3> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],0),([(c,1)],3),([(c,1)],4)], [([],4),([],6)]> joinable by a reduction of rules <[([(c,1)],0),([(c,1)],3),([(c,1)],4)], [([],2),([],6)]> joinable by a reduction of rules <[([(c,1)],0),([(c,1)],3),([(c,1)],2)], [([],4),([],6)]> joinable by a reduction of rules <[([(c,1)],0),([(c,1)],3),([(c,1)],2)], [([],2),([],6)]> joinable by a reduction of rules <[], [([],4),([],6),([(c,1)],1)]> joinable by a reduction of rules <[], [([],2),([],6),([(c,1)],1)]> joinable by a reduction of rules <[([(c,1)],0)], [([],4),([],6),([(c,1)],6)]> joinable by a reduction of rules <[([(c,1)],0)], [([],2),([],6),([(c,1)],6)]> joinable by a reduction of rules <[([(c,1)],0),([(c,1)],3),([(c,1)],4)], [([],4),([],1),([],0)]> joinable by a reduction of rules <[([(c,1)],0),([(c,1)],3),([(c,1)],4)], [([],2),([],1),([],0)]> joinable by a reduction of rules <[([(c,1)],0),([(c,1)],3),([(c,1)],2)], [([],4),([],1),([],0)]> joinable by a reduction of rules <[([(c,1)],0),([(c,1)],3),([(c,1)],2)], [([],2),([],1),([],0)]> Critical Pair by Rules <2, 3> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],6),([(c,1)],3)], [([],4),([],6)]> joinable by a reduction of rules <[([(c,1)],6),([(c,1)],3)], [([],2),([],6)]> Critical Pair by Rules <4, 3> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],6),([(c,1)],3)], [([],4),([],6)]> joinable by a reduction of rules <[([(c,1)],6),([(c,1)],3)], [([],2),([],6)]> Critical Pair by Rules <6, 3> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],3),([(c,1)],4)], [([],4),([],6)]> joinable by a reduction of rules <[([(c,1)],3),([(c,1)],4)], [([],2),([],6)]> joinable by a reduction of rules <[([(c,1)],3),([(c,1)],2)], [([],4),([],6)]> joinable by a reduction of rules <[([(c,1)],3),([(c,1)],2)], [([],2),([],6)]> Critical Pair by Rules <7, 3> preceded by [(c,1)] joinable by a reduction of rules <[], [([(b,1)],3),([],7)]> Critical Pair by Rules <0, 4> preceded by [(b,1)] joinable by a reduction of rules <[([(b,1)],5),([],4)], []> joinable by a reduction of rules <[([(b,1)],5),([],2)], []> joinable by a reduction of rules <[([(b,1)],5)], [([],6),([],3)]> Critical Pair by Rules <3, 4> preceded by [(b,1)] joinable by a reduction of rules <[([],7)], [([],6),([(c,1)],7)]> joinable by a reduction of rules <[([(b,1)],4),([(b,1)],6)], [([],6),([],3)]> joinable by a reduction of rules <[([(b,1)],2),([(b,1)],6)], [([],6),([],3)]> Critical Pair by Rules <5, 4> preceded by [(b,1)] joinable by a reduction of rules <[([(b,1)],0),([],4)], []> joinable by a reduction of rules <[([(b,1)],0),([],2)], []> joinable by a reduction of rules <[([(b,1)],0)], [([],6),([],3)]> Critical Pair by Rules <1, 5> preceded by [(c,1)] joinable by a reduction of rules <[], [([],0),([(c,1)],1)]> joinable by a reduction of rules <[([(c,1)],0)], [([],0),([(c,1)],6)]> Critical Pair by Rules <2, 5> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],6),([(c,1)],3)], [([],0)]> joinable by a reduction of rules <[], [([],0),([(c,1)],4)]> joinable by a reduction of rules <[], [([],0),([(c,1)],2)]> Critical Pair by Rules <4, 5> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],6),([(c,1)],3)], [([],0)]> joinable by a reduction of rules <[], [([],0),([(c,1)],4)]> joinable by a reduction of rules <[], [([],0),([(c,1)],2)]> Critical Pair by Rules <6, 5> preceded by [(c,1)] joinable by a reduction of rules <[([(c,1)],3),([(c,1)],4)], [([],0)]> joinable by a reduction of rules <[([(c,1)],3),([(c,1)],2)], [([],0)]> joinable by a reduction of rules <[], [([],0),([(c,1)],6)]> joinable by a reduction of rules <[([(c,1)],5)], [([],0),([(c,1)],1)]> Critical Pair by Rules <7, 5> preceded by [(c,1)] joinable by a reduction of rules <[], [([],0),([(c,1)],7)]> Critical Pair by Rules <1, 7> preceded by [(b,1)] joinable by a reduction of rules <[([],4),([],6),([(c,1)],6)], [([(c,1)],0)]> joinable by a reduction of rules <[([],4),([],6),([(c,1)],1)], []> joinable by a reduction of rules <[([],2),([],6),([(c,1)],6)], [([(c,1)],0)]> joinable by a reduction of rules <[([],2),([],6),([(c,1)],1)], []> joinable by a reduction of rules <[([],4),([],6)], [([(c,1)],0),([(c,1)],3),([(c,1)],4)]> joinable by a reduction of rules <[([],4),([],6)], [([(c,1)],0),([(c,1)],3),([(c,1)],2)]> joinable by a reduction of rules <[([],2),([],6)], [([(c,1)],0),([(c,1)],3),([(c,1)],4)]> joinable by a reduction of rules <[([],2),([],6)], [([(c,1)],0),([(c,1)],3),([(c,1)],2)]> joinable by a reduction of rules <[([],4),([],1),([],0)], [([(c,1)],0),([(c,1)],3),([(c,1)],4)]> joinable by a reduction of rules <[([],4),([],1),([],0)], [([(c,1)],0),([(c,1)],3),([(c,1)],2)]> joinable by a reduction of rules <[([],2),([],1),([],0)], [([(c,1)],0),([(c,1)],3),([(c,1)],4)]> joinable by a reduction of rules <[([],2),([],1),([],0)], [([(c,1)],0),([(c,1)],3),([(c,1)],2)]> Critical Pair by Rules <2, 7> preceded by [(b,1)] joinable by a reduction of rules <[([(b,1)],6),([(b,1)],3),([],7)], []> Critical Pair by Rules <4, 7> preceded by [(b,1)] joinable by a reduction of rules <[([(b,1)],6),([(b,1)],3),([],7)], []> Critical Pair by Rules <6, 7> preceded by [(b,1)] joinable by a reduction of rules <[([(b,1)],3),([(b,1)],4),([],7)], []> joinable by a reduction of rules <[([(b,1)],3),([(b,1)],2),([],7)], []> joinable by a reduction of rules <[([(b,1)],5),([],4),([],6)], [([(c,1)],0),([(c,1)],3),([(c,1)],4)]> joinable by a reduction of rules <[([(b,1)],5),([],4),([],6)], [([(c,1)],0),([(c,1)],3),([(c,1)],2)]> joinable by a reduction of rules <[([(b,1)],5),([],2),([],6)], [([(c,1)],0),([(c,1)],3),([(c,1)],4)]> joinable by a reduction of rules <[([(b,1)],5),([],2),([],6)], [([(c,1)],0),([(c,1)],3),([(c,1)],2)]> Critical Pair by Rules <7, 7> preceded by [(b,1)] joinable by a reduction of rules <[([],4),([],6)], [([(c,1)],3)]> joinable by a reduction of rules <[([],2),([],6)], [([(c,1)],3)]> joinable by a reduction of rules <[], [([(c,1)],3),([],3)]> joinable by a reduction of rules <[([],4),([],1)], [([(c,1)],3),([],5)]> joinable by a reduction of rules <[([],2),([],1)], [([(c,1)],3),([],5)]> Critical Pair by Rules <6, 1> preceded by [] joinable by a reduction of rules <[([],5)], []> joinable by a reduction of rules <[], [([],0)]> Critical Pair by Rules <4, 2> preceded by [] joinable by a reduction of rules <[], []> Critical Pair by Rules <5, 3> preceded by [] joinable by a reduction of rules <[([],0),([],3)], []> joinable by a reduction of rules <[], [([],4),([],1)]> joinable by a reduction of rules <[], [([],2),([],1)]> joinable by a reduction of rules <[([],0)], [([],4),([],6)]> joinable by a reduction of rules <[([],0)], [([],2),([],6)]> 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... STEP: 1 (parallel) S: [ b(a(?x)) -> c(a(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> b(c(?x)), b(c(?x)) -> b(a(?x)), b(a(?x)) -> c(b(?x)), b(b(?x)) -> c(c(?x)) ] P: [ c(a(?x)) -> c(b(?x)), c(b(?x)) -> c(a(?x)) ] S: unknown termination failure(Step 1) STEP: 2 (linear) S: [ b(a(?x)) -> c(a(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> b(c(?x)), b(c(?x)) -> b(a(?x)), b(a(?x)) -> c(b(?x)), b(b(?x)) -> c(c(?x)) ] P: [ c(a(?x)) -> c(b(?x)), c(b(?x)) -> c(a(?x)) ] S: unknown termination failure(Step 2) STEP: 3 (relative) S: [ b(a(?x)) -> c(a(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> b(c(?x)), b(c(?x)) -> b(a(?x)), b(a(?x)) -> c(b(?x)), b(b(?x)) -> c(c(?x)) ] P: [ c(a(?x)) -> c(b(?x)), c(b(?x)) -> c(a(?x)) ] Check relative termination: [ b(a(?x)) -> c(a(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> b(c(?x)), b(c(?x)) -> b(a(?x)), b(a(?x)) -> c(b(?x)), b(b(?x)) -> c(c(?x)) ] [ c(a(?x)) -> c(b(?x)), c(b(?x)) -> c(a(?x)) ] Polynomial Interpretation: a:= (1)*x1 b:= (1)*x1 c:= (1)+(1)*x1 retract b(c(?x)) -> b(a(?x)) retract b(c(?x)) -> b(a(?x)) Polynomial Interpretation: a:= (1)*x1 b:= (2)+(1)*x1 c:= (1)*x1 retract b(a(?x)) -> c(a(?x)) retract b(c(?x)) -> b(a(?x)) retract b(c(?x)) -> b(a(?x)) retract b(b(?x)) -> c(c(?x)) retract c(b(?x)) -> c(a(?x)) Polynomial Interpretation: a:= (2)+(2)*x1*x1 b:= (1)*x1 c:= (1)*x1*x1 retract b(a(?x)) -> c(a(?x)) retract b(c(?x)) -> b(a(?x)) retract b(c(?x)) -> b(a(?x)) retract b(a(?x)) -> c(b(?x)) retract b(b(?x)) -> c(c(?x)) retract c(a(?x)) -> c(b(?x)) retract c(b(?x)) -> c(a(?x)) Polynomial Interpretation: a:= (2)*x1*x1 b:= (1)+(1)*x1 c:= (3)+(1)*x1+(1)*x1*x1 relatively terminating S/P: relatively terminating check CP condition: failed failure(Step 3) failure(no possibility remains) unknown Reduction-Preserving Completion Direct Methods: Can't judge Try Persistent Decomposition for... [ c(a(?x)) -> c(b(?x)), b(a(?x)) -> c(a(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> b(c(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> c(a(?x)), b(a(?x)) -> c(b(?x)), b(b(?x)) -> c(c(?x)) ] Sort Assignment: a : 15=>15 b : 15=>15 c : 15=>15 maximal types: {15} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ c(a(?x)) -> c(b(?x)), b(a(?x)) -> c(a(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> b(c(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> c(a(?x)), b(a(?x)) -> c(b(?x)), b(b(?x)) -> c(c(?x)) ] Layer Preserving Decomposition failed: Can't judge Try Commutative Decomposition for... [ c(a(?x)) -> c(b(?x)), b(a(?x)) -> c(a(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> b(c(?x)), b(c(?x)) -> b(a(?x)), c(b(?x)) -> c(a(?x)), b(a(?x)) -> c(b(?x)), b(b(?x)) -> c(c(?x)) ] Outside Critical Pair: by Rules <6, 1> develop reducts from lhs term... <{5}, c(a(?x_6))> <{3}, b(c(?x_6))> <{}, c(b(?x_6))> develop reducts from rhs term... <{0}, c(b(?x_6))> <{}, c(a(?x_6))> Outside Critical Pair: by Rules <4, 2> develop reducts from lhs term... <{6}, c(b(?x_4))> <{1}, c(a(?x_4))> <{}, b(a(?x_4))> develop reducts from rhs term... <{6}, c(b(?x_4))> <{1}, c(a(?x_4))> <{}, b(a(?x_4))> Outside Critical Pair: by Rules <5, 3> develop reducts from lhs term... <{0}, c(b(?x_5))> <{}, c(a(?x_5))> develop reducts from rhs term... <{4}, b(a(?x_5))> <{2}, b(a(?x_5))> <{}, b(c(?x_5))> Inside Critical Pair: by Rules <0, 2> develop reducts from lhs term... <{4}, b(a(b(?x)))> <{2}, b(a(b(?x)))> <{5}, b(c(a(?x)))> <{3}, b(b(c(?x)))> <{}, b(c(b(?x)))> develop reducts from rhs term... <{6}, c(b(a(?x)))> <{1}, c(a(a(?x)))> <{}, b(a(a(?x)))> Inside Critical Pair: by Rules <3, 2> develop reducts from lhs term... <{7}, c(c(c(?x_3)))> <{4}, b(b(a(?x_3)))> <{2}, b(b(a(?x_3)))> <{}, b(b(c(?x_3)))> develop reducts from rhs term... <{6}, c(b(b(?x_3)))> <{1}, c(a(b(?x_3)))> <{}, b(a(b(?x_3)))> Inside Critical Pair: by Rules <5, 2> develop reducts from lhs term... <{4}, b(a(a(?x_5)))> <{2}, b(a(a(?x_5)))> <{0}, b(c(b(?x_5)))> <{}, b(c(a(?x_5)))> develop reducts from rhs term... <{6}, c(b(b(?x_5)))> <{1}, c(a(b(?x_5)))> <{}, b(a(b(?x_5)))> Inside Critical Pair: by Rules <1, 3> develop reducts from lhs term... <{0}, c(c(b(?x_1)))> <{}, c(c(a(?x_1)))> develop reducts from rhs term... <{4}, b(a(a(?x_1)))> <{2}, b(a(a(?x_1)))> <{0}, b(c(b(?x_1)))> <{}, b(c(a(?x_1)))> Inside Critical Pair: by Rules <2, 3> develop reducts from lhs term... <{5}, c(a(a(?x_2)))> <{3}, b(c(a(?x_2)))> <{6}, c(c(b(?x_2)))> <{1}, c(c(a(?x_2)))> <{}, c(b(a(?x_2)))> develop reducts from rhs term... <{4}, b(a(c(?x_2)))> <{2}, b(a(c(?x_2)))> <{}, b(c(c(?x_2)))> Inside Critical Pair: by Rules <4, 3> develop reducts from lhs term... <{5}, c(a(a(?x_4)))> <{3}, b(c(a(?x_4)))> <{6}, c(c(b(?x_4)))> <{1}, c(c(a(?x_4)))> <{}, c(b(a(?x_4)))> develop reducts from rhs term... <{4}, b(a(c(?x_4)))> <{2}, b(a(c(?x_4)))> <{}, b(c(c(?x_4)))> Inside Critical Pair: by Rules <6, 3> develop reducts from lhs term... <{5}, c(c(a(?x_6)))> <{3}, c(b(c(?x_6)))> <{}, c(c(b(?x_6)))> develop reducts from rhs term... <{4}, b(a(a(?x_6)))> <{2}, b(a(a(?x_6)))> <{0}, b(c(b(?x_6)))> <{}, b(c(a(?x_6)))> Inside Critical Pair: by Rules <7, 3> develop reducts from lhs term... <{}, c(c(c(?x_7)))> develop reducts from rhs term... <{4}, b(a(b(?x_7)))> <{2}, b(a(b(?x_7)))> <{5}, b(c(a(?x_7)))> <{3}, b(b(c(?x_7)))> <{}, b(c(b(?x_7)))> Inside Critical Pair: by Rules <0, 4> develop reducts from lhs term... <{4}, b(a(b(?x)))> <{2}, b(a(b(?x)))> <{5}, b(c(a(?x)))> <{3}, b(b(c(?x)))> <{}, b(c(b(?x)))> develop reducts from rhs term... <{6}, c(b(a(?x)))> <{1}, c(a(a(?x)))> <{}, b(a(a(?x)))> Inside Critical Pair: by Rules <3, 4> develop reducts from lhs term... <{7}, c(c(c(?x_3)))> <{4}, b(b(a(?x_3)))> <{2}, b(b(a(?x_3)))> <{}, b(b(c(?x_3)))> develop reducts from rhs term... <{6}, c(b(b(?x_3)))> <{1}, c(a(b(?x_3)))> <{}, b(a(b(?x_3)))> Inside Critical Pair: by Rules <5, 4> develop reducts from lhs term... <{4}, b(a(a(?x_5)))> <{2}, b(a(a(?x_5)))> <{0}, b(c(b(?x_5)))> <{}, b(c(a(?x_5)))> develop reducts from rhs term... <{6}, c(b(b(?x_5)))> <{1}, c(a(b(?x_5)))> <{}, b(a(b(?x_5)))> Inside Critical Pair: by Rules <1, 5> develop reducts from lhs term... <{0}, c(c(b(?x_1)))> <{}, c(c(a(?x_1)))> develop reducts from rhs term... <{0}, c(b(a(?x_1)))> <{}, c(a(a(?x_1)))> Inside Critical Pair: by Rules <2, 5> develop reducts from lhs term... <{5}, c(a(a(?x_2)))> <{3}, b(c(a(?x_2)))> <{6}, c(c(b(?x_2)))> <{1}, c(c(a(?x_2)))> <{}, c(b(a(?x_2)))> develop reducts from rhs term... <{0}, c(b(c(?x_2)))> <{}, c(a(c(?x_2)))> Inside Critical Pair: by Rules <4, 5> develop reducts from lhs term... <{5}, c(a(a(?x_4)))> <{3}, b(c(a(?x_4)))> <{6}, c(c(b(?x_4)))> <{1}, c(c(a(?x_4)))> <{}, c(b(a(?x_4)))> develop reducts from rhs term... <{0}, c(b(c(?x_4)))> <{}, c(a(c(?x_4)))> Inside Critical Pair: by Rules <6, 5> develop reducts from lhs term... <{5}, c(c(a(?x_6)))> <{3}, c(b(c(?x_6)))> <{}, c(c(b(?x_6)))> develop reducts from rhs term... <{0}, c(b(a(?x_6)))> <{}, c(a(a(?x_6)))> Inside Critical Pair: by Rules <7, 5> develop reducts from lhs term... <{}, c(c(c(?x_7)))> develop reducts from rhs term... <{0}, c(b(b(?x_7)))> <{}, c(a(b(?x_7)))> Inside Critical Pair: by Rules <1, 7> develop reducts from lhs term... <{4}, b(a(a(?x_1)))> <{2}, b(a(a(?x_1)))> <{0}, b(c(b(?x_1)))> <{}, b(c(a(?x_1)))> develop reducts from rhs term... <{0}, c(c(b(?x_1)))> <{}, c(c(a(?x_1)))> Inside Critical Pair: by Rules <2, 7> develop reducts from lhs term... <{7}, c(c(a(?x_2)))> <{6}, b(c(b(?x_2)))> <{1}, b(c(a(?x_2)))> <{}, b(b(a(?x_2)))> develop reducts from rhs term... <{}, c(c(c(?x_2)))> Inside Critical Pair: by Rules <4, 7> develop reducts from lhs term... <{7}, c(c(a(?x_4)))> <{6}, b(c(b(?x_4)))> <{1}, b(c(a(?x_4)))> <{}, b(b(a(?x_4)))> develop reducts from rhs term... <{}, c(c(c(?x_4)))> Inside Critical Pair: by Rules <6, 7> develop reducts from lhs term... <{4}, b(a(b(?x_6)))> <{2}, b(a(b(?x_6)))> <{5}, b(c(a(?x_6)))> <{3}, b(b(c(?x_6)))> <{}, b(c(b(?x_6)))> develop reducts from rhs term... <{0}, c(c(b(?x_6)))> <{}, c(c(a(?x_6)))> Commutative Decomposition failed: Can't judge No further decomposition possible Combined result: Can't judge 1018.trs: Failure(unknown CR) MAYBE (6045 msec.)