MAYBE
(ignored inputs)COMMENT submitted by: Johannes Waldmann
Rewrite Rules:
   [ c(b(?x)) -> b(c(?x)),
     c(c(?x)) -> c(b(?x)),
     b(b(?x)) -> c(a(?x)),
     a(b(?x)) -> b(b(?x)),
     a(c(?x)) -> c(c(?x)) ]
Apply Direct Methods...
Inner CPs:
   [ c(c(a(?x_2))) = b(c(b(?x_2))),
     c(b(c(?x))) = c(b(b(?x))),
     a(c(a(?x_2))) = b(b(b(?x_2))),
     a(b(c(?x))) = c(c(b(?x))),
     a(c(b(?x_1))) = c(c(c(?x_1))),
     c(c(b(?x))) = c(b(c(?x))),
     b(c(a(?x))) = c(a(b(?x))) ]
Outer CPs:
   [  ]
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:
   [ c(c(a(?x_3))) = b(c(b(?x_3))),
     c(b(c(a(?x_3)))) = c(b(c(b(?x_3)))),
     c(c(c(a(?x_3)))) = a(b(c(b(?x_3)))),
     c(b(b(?x))) = c(b(c(?x))),
     c(c(b(?x))) = a(b(c(?x))),
     c(c(b(?x_1))) = c(b(c(?x_1))),
     c(b(c(?x_2))) = c(b(b(?x_2))),
     c(b(c(b(?x_1)))) = c(c(b(c(?x_1)))),
     c(b(b(c(?x_2)))) = c(c(b(b(?x_2)))),
     c(c(c(b(?x_1)))) = a(c(b(c(?x_1)))),
     c(c(b(c(?x_2)))) = a(c(b(b(?x_2)))),
     c(b(c(?x))) = c(c(b(?x))),
     c(c(c(?x))) = a(c(b(?x))),
     b(c(a(?x_1))) = c(a(b(?x_1))),
     c(a(c(a(?x_1)))) = b(c(a(b(?x_1)))),
     b(c(c(a(?x_1)))) = c(c(a(b(?x_1)))),
     b(b(c(a(?x_1)))) = a(c(a(b(?x_1)))),
     c(a(b(?x))) = b(c(a(?x))),
     b(c(b(?x))) = c(c(a(?x))),
     b(b(b(?x))) = a(c(a(?x))),
     a(c(a(?x_4))) = b(b(b(?x_4))),
     a(b(c(?x_2))) = c(c(b(?x_2))),
     a(c(b(?x_3))) = c(c(c(?x_3))) ]
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 <c(c(a(?x_2))), b(c(b(?x_2)))> by Rules <2, 0> preceded by [(c,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 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(b(?x)) -> b(c(?x)),
     c(c(?x)) -> c(b(?x)),
     b(b(?x)) -> c(a(?x)),
     a(b(?x)) -> b(b(?x)),
     a(c(?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...
   [ c(b(?x)) -> b(c(?x)),
     c(c(?x)) -> c(b(?x)),
     b(b(?x)) -> c(a(?x)),
     a(b(?x)) -> b(b(?x)),
     a(c(?x)) -> c(c(?x)) ]
Sort Assignment:
 a : 12=>12
 b : 12=>12
 c : 12=>12
maximal types: {12}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ c(b(?x)) -> b(c(?x)),
     c(c(?x)) -> c(b(?x)),
     b(b(?x)) -> c(a(?x)),
     a(b(?x)) -> b(b(?x)),
     a(c(?x)) -> c(c(?x)) ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ c(b(?x)) -> b(c(?x)),
     c(c(?x)) -> c(b(?x)),
     b(b(?x)) -> c(a(?x)),
     a(b(?x)) -> b(b(?x)),
     a(c(?x)) -> c(c(?x)) ]
Inside Critical Pair: <c(c(a(?x_2))), b(c(b(?x_2)))> by Rules <2, 0>
develop reducts from lhs term...
<{1}, c(b(a(?x_2)))>
<{}, c(c(a(?x_2)))>
develop reducts from rhs term...
<{0}, b(b(c(?x_2)))>
<{}, b(c(b(?x_2)))>
Inside Critical Pair: <c(b(c(?x))), c(b(b(?x)))> by Rules <0, 1>
develop reducts from lhs term...
<{0}, b(c(c(?x)))>
<{}, c(b(c(?x)))>
develop reducts from rhs term...
<{0}, b(c(b(?x)))>
<{2}, c(c(a(?x)))>
<{}, c(b(b(?x)))>
Inside Critical Pair: <a(c(a(?x_2))), b(b(b(?x_2)))> by Rules <2, 3>
develop reducts from lhs term...
<{4}, c(c(a(?x_2)))>
<{}, a(c(a(?x_2)))>
develop reducts from rhs term...
<{2}, c(a(b(?x_2)))>
<{2}, b(c(a(?x_2)))>
<{}, b(b(b(?x_2)))>
Inside Critical Pair: <a(b(c(?x))), c(c(b(?x)))> by Rules <0, 4>
develop reducts from lhs term...
<{3}, b(b(c(?x)))>
<{}, a(b(c(?x)))>
develop reducts from rhs term...
<{1}, c(b(b(?x)))>
<{0}, c(b(c(?x)))>
<{}, c(c(b(?x)))>
Inside Critical Pair: <a(c(b(?x_1))), c(c(c(?x_1)))> by Rules <1, 4>
develop reducts from lhs term...
<{4}, c(c(b(?x_1)))>
<{0}, a(b(c(?x_1)))>
<{}, a(c(b(?x_1)))>
develop reducts from rhs term...
<{1}, c(b(c(?x_1)))>
<{1}, c(c(b(?x_1)))>
<{}, c(c(c(?x_1)))>
Commutative Decomposition failed: Can't judge
No further decomposition possible


Combined result: Can't judge
987.trs: Failure(unknown CR)
(1669 msec.)