(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
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)
MAYBE
(6441 msec.)