MAYBE
(ignored inputs)COMMENT the following rules are removed from the original TRS a ( a ( x ) ) -> a ( a ( x ) )
Rewrite Rules:
[ a(c(?x)) -> c(a(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> c(b(?x)),
b(b(?x)) -> a(c(?x)),
b(a(?x)) -> a(c(?x)),
c(b(?x)) -> a(b(?x)),
a(a(?x)) -> c(a(?x)) ]
Apply Direct Methods...
Inner CPs:
[ a(c(b(?x_3))) = c(a(a(?x_3))),
a(a(b(?x_6))) = c(a(b(?x_6))),
a(a(c(?x_4))) = c(a(b(?x_4))),
a(a(c(?x_5))) = c(a(a(?x_5))),
a(c(a(?x))) = a(c(c(?x))),
a(c(a(?x_1))) = a(c(b(?x_1))),
a(c(a(?x_7))) = a(c(a(?x_7))),
c(c(a(?x))) = c(b(c(?x))),
c(c(a(?x_1))) = c(b(b(?x_1))),
c(a(c(?x_2))) = c(b(a(?x_2))),
c(c(a(?x_7))) = c(b(a(?x_7))),
b(a(c(?x_5))) = a(c(a(?x_5))),
b(c(a(?x))) = a(c(c(?x))),
b(c(a(?x_1))) = a(c(b(?x_1))),
b(a(c(?x_2))) = a(c(a(?x_2))),
b(c(a(?x_7))) = a(c(a(?x_7))),
c(a(c(?x_4))) = a(b(b(?x_4))),
c(a(c(?x_5))) = a(b(a(?x_5))),
a(c(a(?x))) = c(a(c(?x))),
a(c(a(?x_1))) = c(a(b(?x_1))),
a(a(c(?x_2))) = c(a(a(?x_2))),
a(a(c(?x))) = a(c(a(?x))),
b(a(c(?x))) = a(c(b(?x))),
a(c(a(?x))) = c(a(a(?x))) ]
Outer CPs:
[ a(c(?x_2)) = c(a(?x_2)) ]
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:
[ a(c(b(?x_4))) = c(a(a(?x_4))),
a(a(b(?x_7))) = c(a(b(?x_7))),
a(c(c(b(?x_4)))) = a(c(a(a(?x_4)))),
a(c(a(b(?x_7)))) = a(c(a(b(?x_7)))),
c(b(c(b(?x_4)))) = c(c(a(a(?x_4)))),
c(b(a(b(?x_7)))) = c(c(a(b(?x_7)))),
a(c(c(b(?x_4)))) = b(c(a(a(?x_4)))),
a(c(a(b(?x_7)))) = b(c(a(b(?x_7)))),
c(a(c(b(?x_4)))) = a(c(a(a(?x_4)))),
c(a(a(b(?x_7)))) = a(c(a(b(?x_7)))),
a(c(c(?x))) = a(c(a(?x))),
c(b(c(?x))) = c(c(a(?x))),
a(c(c(?x))) = b(c(a(?x))),
c(a(c(?x))) = a(c(a(?x))),
a(a(c(?x_5))) = c(a(b(?x_5))),
a(a(c(?x_6))) = c(a(a(?x_6))),
a(c(a(c(?x_5)))) = a(c(a(b(?x_5)))),
a(c(a(c(?x_6)))) = a(c(a(a(?x_6)))),
c(b(a(c(?x_5)))) = c(c(a(b(?x_5)))),
c(b(a(c(?x_6)))) = c(c(a(a(?x_6)))),
a(c(a(c(?x_5)))) = b(c(a(b(?x_5)))),
a(c(a(c(?x_6)))) = b(c(a(a(?x_6)))),
c(a(a(c(?x_5)))) = a(c(a(b(?x_5)))),
c(a(a(c(?x_6)))) = a(c(a(a(?x_6)))),
a(c(b(?x))) = a(c(a(?x))),
c(b(b(?x))) = c(c(a(?x))),
a(c(b(?x))) = b(c(a(?x))),
c(a(b(?x))) = a(c(a(?x))),
c(a(?x)) = a(c(?x)),
a(a(c(?x_1))) = a(c(a(?x_1))),
a(c(a(?x_2))) = a(c(c(?x_2))),
a(c(a(?x_3))) = a(c(b(?x_3))),
a(c(a(?x_8))) = a(c(a(?x_8))),
a(c(a(c(?x_1)))) = a(a(c(a(?x_1)))),
a(c(c(a(?x_2)))) = a(a(c(c(?x_2)))),
a(c(c(a(?x_3)))) = a(a(c(b(?x_3)))),
a(c(c(a(?x_8)))) = a(a(c(a(?x_8)))),
c(b(a(c(?x_1)))) = c(a(c(a(?x_1)))),
c(b(c(a(?x_2)))) = c(a(c(c(?x_2)))),
c(b(c(a(?x_3)))) = c(a(c(b(?x_3)))),
c(b(c(a(?x_8)))) = c(a(c(a(?x_8)))),
a(c(a(c(?x_1)))) = b(a(c(a(?x_1)))),
a(c(c(a(?x_2)))) = b(a(c(c(?x_2)))),
a(c(c(a(?x_3)))) = b(a(c(b(?x_3)))),
a(c(c(a(?x_8)))) = b(a(c(a(?x_8)))),
c(a(a(c(?x_1)))) = a(a(c(a(?x_1)))),
c(a(c(a(?x_2)))) = a(a(c(c(?x_2)))),
c(a(c(a(?x_3)))) = a(a(c(b(?x_3)))),
c(a(c(a(?x_8)))) = a(a(c(a(?x_8)))),
a(c(a(?x))) = a(a(c(?x))),
c(b(a(?x))) = c(a(c(?x))),
a(c(a(?x))) = b(a(c(?x))),
c(a(a(?x))) = a(a(c(?x))),
c(c(a(?x_2))) = c(b(c(?x_2))),
c(c(a(?x_3))) = c(b(b(?x_3))),
c(a(c(?x_4))) = c(b(a(?x_4))),
c(c(a(?x_8))) = c(b(a(?x_8))),
c(a(c(a(?x_2)))) = a(c(b(c(?x_2)))),
c(a(c(a(?x_3)))) = a(c(b(b(?x_3)))),
c(a(a(c(?x_4)))) = a(c(b(a(?x_4)))),
c(a(c(a(?x_8)))) = a(c(b(a(?x_8)))),
c(a(a(?x))) = a(c(b(?x))),
b(a(c(?x_1))) = a(c(b(?x_1))),
b(a(c(?x_6))) = a(c(a(?x_6))),
a(c(a(c(?x_1)))) = b(a(c(b(?x_1)))),
c(a(a(c(?x_1)))) = a(a(c(b(?x_1)))),
a(b(a(c(?x_1)))) = c(a(c(b(?x_1)))),
a(b(a(c(?x_6)))) = c(a(c(a(?x_6)))),
a(c(b(?x))) = b(a(c(?x))),
c(a(b(?x))) = a(a(c(?x))),
a(b(b(?x))) = c(a(c(?x))),
b(c(a(?x_2))) = a(c(c(?x_2))),
b(c(a(?x_3))) = a(c(b(?x_3))),
b(c(a(?x_8))) = a(c(a(?x_8))),
a(b(c(a(?x_2)))) = c(a(c(c(?x_2)))),
a(b(c(a(?x_3)))) = c(a(c(b(?x_3)))),
a(b(c(a(?x_8)))) = c(a(c(a(?x_8)))),
a(b(a(?x))) = c(a(c(?x))),
c(a(c(?x_6))) = a(b(b(?x_6))),
c(a(c(?x_7))) = a(b(a(?x_7))),
c(a(a(c(?x_6)))) = a(a(b(b(?x_6)))),
c(a(a(c(?x_7)))) = a(a(b(a(?x_7)))),
c(a(b(?x))) = a(a(b(?x))),
a(c(?x)) = c(a(?x)),
a(c(a(?x_1))) = c(a(a(?x_1))),
a(c(a(?x_2))) = c(a(c(?x_2))),
a(c(a(?x_3))) = c(a(b(?x_3))),
c(a(c(a(?x_1)))) = a(c(a(a(?x_1)))),
c(a(c(a(?x_2)))) = a(c(a(c(?x_2)))),
c(a(c(a(?x_3)))) = a(c(a(b(?x_3)))),
a(c(c(a(?x_1)))) = a(c(a(a(?x_1)))),
a(c(c(a(?x_2)))) = a(c(a(c(?x_2)))),
a(c(c(a(?x_3)))) = a(c(a(b(?x_3)))),
c(b(c(a(?x_1)))) = c(c(a(a(?x_1)))),
c(b(c(a(?x_2)))) = c(c(a(c(?x_2)))),
c(b(c(a(?x_3)))) = c(c(a(b(?x_3)))),
a(c(c(a(?x_1)))) = b(c(a(a(?x_1)))),
a(c(c(a(?x_2)))) = b(c(a(c(?x_2)))),
a(c(c(a(?x_3)))) = b(c(a(b(?x_3)))),
c(a(a(?x))) = a(c(a(?x))),
c(b(a(?x))) = c(c(a(?x))),
a(c(a(?x))) = b(c(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 [(a,1)]
joinable by a reduction of rules <[([],0),([(c,1)],1)], [([(c,1)],7)]>
joinable by a reduction of rules <[([],0),([(c,1)],1)], [([(c,1)],2),([(c,1)],0)]>
Critical Pair by Rules <6, 0> preceded by [(a,1)]
joinable by a reduction of rules <[([],7)], []>
Critical Pair by Rules <4, 1> preceded by [(a,1)]
joinable by a reduction of rules <[([],7),([(c,1)],0)], [([(c,1)],1)]>
joinable by a reduction of rules <[([],7)], [([],3),([(c,1)],4)]>
joinable by a reduction of rules <[([],2),([],0)], [([],3),([(c,1)],4)]>
Critical Pair by Rules <5, 1> preceded by [(a,1)]
joinable by a reduction of rules <[([],7)], [([(c,1)],2)]>
Critical Pair by Rules <0, 2> preceded by [(a,1)]
joinable by a reduction of rules <[([],0),([(c,1)],2)], [([],0)]>
joinable by a reduction of rules <[([],0),([(c,1)],7)], [([],0),([(c,1)],0)]>
Critical Pair by Rules <1, 2> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],3)], []>
Critical Pair by Rules <7, 2> preceded by [(a,1)]
joinable by a reduction of rules <[], []>
Critical Pair by Rules <0, 3> preceded by [(c,1)]
joinable by a reduction of rules <[], [([],6),([],1),([(c,1)],0)]>
Critical Pair by Rules <1, 3> preceded by [(c,1)]
joinable by a reduction of rules <[], [([(c,1)],4),([(c,1)],0)]>
joinable by a reduction of rules <[([(c,1)],3),([(c,1)],6)], [([],6),([],1)]>
Critical Pair by Rules <2, 3> preceded by [(c,1)]
joinable by a reduction of rules <[], [([(c,1)],5)]>
Critical Pair by Rules <7, 3> preceded by [(c,1)]
joinable by a reduction of rules <[], [([(c,1)],5),([(c,1)],0)]>
Critical Pair by Rules <5, 4> preceded by [(b,1)]
joinable by a reduction of rules <[([],5),([],0)], [([],0),([(c,1)],2)]>
Critical Pair by Rules <0, 5> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],3),([(b,1)],6),([],5),([],0)], [([],0),([(c,1)],0),([(c,1)],3),([(c,1)],6)]>
Critical Pair by Rules <1, 5> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],3),([(b,1)],6),([],5)], []>
Critical Pair by Rules <2, 5> preceded by [(b,1)]
joinable by a reduction of rules <[([],5),([],0)], [([],0),([(c,1)],2)]>
Critical Pair by Rules <7, 5> preceded by [(b,1)]
joinable by a reduction of rules <[([(b,1)],3),([(b,1)],6),([],5)], [([(a,1)],3)]>
Critical Pair by Rules <4, 6> preceded by [(c,1)]
joinable by a reduction of rules <[], [([(a,1)],4),([],7)]>
joinable by a reduction of rules <[([(c,1)],0)], [([],1),([(c,1)],1)]>
Critical Pair by Rules <5, 6> preceded by [(c,1)]
joinable by a reduction of rules <[], [([(a,1)],5),([],7)]>
joinable by a reduction of rules <[], [([],1),([(c,1)],2)]>
joinable by a reduction of rules <[([(c,1)],0)], [([],1),([(c,1)],7)]>
Critical Pair by Rules <0, 7> preceded by [(a,1)]
joinable by a reduction of rules <[([],0),([(c,1)],7)], [([(c,1)],0)]>
joinable by a reduction of rules <[([],0),([(c,1)],2)], []>
Critical Pair by Rules <1, 7> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],3),([],0)], []>
joinable by a reduction of rules <[([],0),([(c,1)],7)], [([(c,1)],1)]>
joinable by a reduction of rules <[([],0),([(c,1)],2)], [([],3),([(c,1)],4)]>
Critical Pair by Rules <2, 7> preceded by [(a,1)]
joinable by a reduction of rules <[([],7)], [([(c,1)],2)]>
Critical Pair by Rules <2, 2> preceded by [(a,1)]
joinable by a reduction of rules <[([(a,1)],0)], []>
Critical Pair by Rules <4, 4> preceded by [(b,1)]
joinable by a reduction of rules <[([],5),([],0),([(c,1)],0)], [([],0),([(c,1)],1)]>
joinable by a reduction of rules <[([],5),([],0)], [([],0),([],3),([(c,1)],4)]>
joinable by a reduction of rules <[([],5),([],0),([(c,1)],0)], [([(a,1)],6),([],7),([(c,1)],1)]>
Critical Pair by Rules <7, 7> preceded by [(a,1)]
joinable by a reduction of rules <[([],0)], []>
Critical Pair by Rules <7, 2> preceded by []
joinable by a reduction of rules <[], [([],0)]>
unknown Diagram Decreasing
check Non-Confluence...
obtain 14 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(c(?x)) -> c(a(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> c(b(?x)),
b(b(?x)) -> a(c(?x)),
b(a(?x)) -> a(c(?x)),
c(b(?x)) -> a(b(?x)),
a(a(?x)) -> c(a(?x)) ]
E-part:
[ ]
...failed to find a suitable LPO.
unknown Confluence by Ordered Rewriting
Direct Methods: Can't judge
Try Persistent Decomposition for...
[ a(c(?x)) -> c(a(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> c(b(?x)),
b(b(?x)) -> a(c(?x)),
b(a(?x)) -> a(c(?x)),
c(b(?x)) -> a(b(?x)),
a(a(?x)) -> c(a(?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...
[ a(c(?x)) -> c(a(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> c(b(?x)),
b(b(?x)) -> a(c(?x)),
b(a(?x)) -> a(c(?x)),
c(b(?x)) -> a(b(?x)),
a(a(?x)) -> c(a(?x)) ]
Layer Preserving Decomposition failed: Can't judge
Try Commutative Decomposition for...
[ a(c(?x)) -> c(a(?x)),
a(b(?x)) -> c(a(?x)),
a(a(?x)) -> a(c(?x)),
c(a(?x)) -> c(b(?x)),
b(b(?x)) -> a(c(?x)),
b(a(?x)) -> a(c(?x)),
c(b(?x)) -> a(b(?x)),
a(a(?x)) -> c(a(?x)) ]
Outside Critical Pair: by Rules <7, 2>
develop reducts from lhs term...
<{3}, c(b(?x_7))>
<{}, c(a(?x_7))>
develop reducts from rhs term...
<{0}, c(a(?x_7))>
<{}, a(c(?x_7))>
Inside Critical Pair: by Rules <3, 0>
develop reducts from lhs term...
<{0}, c(a(b(?x_3)))>
<{6}, a(a(b(?x_3)))>
<{}, a(c(b(?x_3)))>
develop reducts from rhs term...
<{3}, c(b(a(?x_3)))>
<{7}, c(c(a(?x_3)))>
<{2}, c(a(c(?x_3)))>
<{}, c(a(a(?x_3)))>
Inside Critical Pair: by Rules <6, 0>
develop reducts from lhs term...
<{7}, c(a(b(?x_6)))>
<{2}, a(c(b(?x_6)))>
<{1}, a(c(a(?x_6)))>
<{}, a(a(b(?x_6)))>
develop reducts from rhs term...
<{3}, c(b(b(?x_6)))>
<{1}, c(c(a(?x_6)))>
<{}, c(a(b(?x_6)))>
Inside Critical Pair: by Rules <4, 1>
develop reducts from lhs term...
<{7}, c(a(c(?x_4)))>
<{2}, a(c(c(?x_4)))>
<{0}, a(c(a(?x_4)))>
<{}, a(a(c(?x_4)))>
develop reducts from rhs term...
<{3}, c(b(b(?x_4)))>
<{1}, c(c(a(?x_4)))>
<{}, c(a(b(?x_4)))>
Inside Critical Pair: by Rules <5, 1>
develop reducts from lhs term...
<{7}, c(a(c(?x_5)))>
<{2}, a(c(c(?x_5)))>
<{0}, a(c(a(?x_5)))>
<{}, a(a(c(?x_5)))>
develop reducts from rhs term...
<{3}, c(b(a(?x_5)))>
<{7}, c(c(a(?x_5)))>
<{2}, c(a(c(?x_5)))>
<{}, c(a(a(?x_5)))>
Inside Critical Pair: by Rules <0, 2>
develop reducts from lhs term...
<{0}, c(a(a(?x)))>
<{3}, a(c(b(?x)))>
<{}, a(c(a(?x)))>
develop reducts from rhs term...
<{0}, c(a(c(?x)))>
<{}, a(c(c(?x)))>
Inside Critical Pair: by Rules <1, 2>
develop reducts from lhs term...
<{0}, c(a(a(?x_1)))>
<{3}, a(c(b(?x_1)))>
<{}, a(c(a(?x_1)))>
develop reducts from rhs term...
<{0}, c(a(b(?x_1)))>
<{6}, a(a(b(?x_1)))>
<{}, a(c(b(?x_1)))>
Inside Critical Pair: by Rules <7, 2>
develop reducts from lhs term...
<{0}, c(a(a(?x_7)))>
<{3}, a(c(b(?x_7)))>
<{}, a(c(a(?x_7)))>
develop reducts from rhs term...
<{0}, c(a(a(?x_7)))>
<{3}, a(c(b(?x_7)))>
<{}, a(c(a(?x_7)))>
Inside Critical Pair: by Rules <0, 3>
develop reducts from lhs term...
<{3}, c(c(b(?x)))>
<{}, c(c(a(?x)))>
develop reducts from rhs term...
<{6}, a(b(c(?x)))>
<{}, c(b(c(?x)))>
Inside Critical Pair: by Rules <1, 3>
develop reducts from lhs term...
<{3}, c(c(b(?x_1)))>
<{}, c(c(a(?x_1)))>
develop reducts from rhs term...
<{6}, a(b(b(?x_1)))>
<{4}, c(a(c(?x_1)))>
<{}, c(b(b(?x_1)))>
Inside Critical Pair: by Rules <2, 3>
develop reducts from lhs term...
<{3}, c(b(c(?x_2)))>
<{0}, c(c(a(?x_2)))>
<{}, c(a(c(?x_2)))>
develop reducts from rhs term...
<{6}, a(b(a(?x_2)))>
<{5}, c(a(c(?x_2)))>
<{}, c(b(a(?x_2)))>
Inside Critical Pair: by Rules <7, 3>
develop reducts from lhs term...
<{3}, c(c(b(?x_7)))>
<{}, c(c(a(?x_7)))>
develop reducts from rhs term...
<{6}, a(b(a(?x_7)))>
<{5}, c(a(c(?x_7)))>
<{}, c(b(a(?x_7)))>
Inside Critical Pair: by Rules <5, 4>
develop reducts from lhs term...
<{5}, a(c(c(?x_5)))>
<{0}, b(c(a(?x_5)))>
<{}, b(a(c(?x_5)))>
develop reducts from rhs term...
<{0}, c(a(a(?x_5)))>
<{3}, a(c(b(?x_5)))>
<{}, a(c(a(?x_5)))>
Inside Critical Pair: by Rules <0, 5>
develop reducts from lhs term...
<{3}, b(c(b(?x)))>
<{}, b(c(a(?x)))>
develop reducts from rhs term...
<{0}, c(a(c(?x)))>
<{}, a(c(c(?x)))>
Inside Critical Pair: by Rules <1, 5>
develop reducts from lhs term...
<{3}, b(c(b(?x_1)))>
<{}, b(c(a(?x_1)))>
develop reducts from rhs term...
<{0}, c(a(b(?x_1)))>
<{6}, a(a(b(?x_1)))>
<{}, a(c(b(?x_1)))>
Inside Critical Pair: by Rules <2, 5>
develop reducts from lhs term...
<{5}, a(c(c(?x_2)))>
<{0}, b(c(a(?x_2)))>
<{}, b(a(c(?x_2)))>
develop reducts from rhs term...
<{0}, c(a(a(?x_2)))>
<{3}, a(c(b(?x_2)))>
<{}, a(c(a(?x_2)))>
Inside Critical Pair: by Rules <7, 5>
develop reducts from lhs term...
<{3}, b(c(b(?x_7)))>
<{}, b(c(a(?x_7)))>
develop reducts from rhs term...
<{0}, c(a(a(?x_7)))>
<{3}, a(c(b(?x_7)))>
<{}, a(c(a(?x_7)))>
Inside Critical Pair: by Rules <4, 6>
develop reducts from lhs term...
<{3}, c(b(c(?x_4)))>
<{0}, c(c(a(?x_4)))>
<{}, c(a(c(?x_4)))>
develop reducts from rhs term...
<{1}, c(a(b(?x_4)))>
<{4}, a(a(c(?x_4)))>
<{}, a(b(b(?x_4)))>
Inside Critical Pair: by Rules <5, 6>
develop reducts from lhs term...
<{3}, c(b(c(?x_5)))>
<{0}, c(c(a(?x_5)))>
<{}, c(a(c(?x_5)))>
develop reducts from rhs term...
<{1}, c(a(a(?x_5)))>
<{5}, a(a(c(?x_5)))>
<{}, a(b(a(?x_5)))>
Inside Critical Pair: by Rules <0, 7>
develop reducts from lhs term...
<{0}, c(a(a(?x)))>
<{3}, a(c(b(?x)))>
<{}, a(c(a(?x)))>
develop reducts from rhs term...
<{3}, c(b(c(?x)))>
<{0}, c(c(a(?x)))>
<{}, c(a(c(?x)))>
Inside Critical Pair: by Rules <1, 7>
develop reducts from lhs term...
<{0}, c(a(a(?x_1)))>
<{3}, a(c(b(?x_1)))>
<{}, a(c(a(?x_1)))>
develop reducts from rhs term...
<{3}, c(b(b(?x_1)))>
<{1}, c(c(a(?x_1)))>
<{}, c(a(b(?x_1)))>
Inside Critical Pair: by Rules <2, 7>
develop reducts from lhs term...
<{7}, c(a(c(?x_2)))>
<{2}, a(c(c(?x_2)))>
<{0}, a(c(a(?x_2)))>
<{}, a(a(c(?x_2)))>
develop reducts from rhs term...
<{3}, c(b(a(?x_2)))>
<{7}, c(c(a(?x_2)))>
<{2}, c(a(c(?x_2)))>
<{}, c(a(a(?x_2)))>
Commutative Decomposition failed: Can't judge
No further decomposition possible
Combined result: Can't judge
/tmp/fileYggbB4.trs: Failure(unknown CR)
(2903 msec.)