MAYBE
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ b(c(?x)) -> a(?x),
     b(b(?x)) -> a(c(?x)),
     a(?x) -> c(b(?x)),
     c(c(c(?x))) -> b(?x) ]
Apply Direct Methods...
Inner CPs:
   [ b(b(?x_3)) = a(c(c(?x_3))),
     b(a(?x)) = a(c(c(?x))),
     b(a(c(?x))) = a(c(b(?x))),
     c(b(?x)) = b(c(?x)),
     c(c(b(?x))) = b(c(c(?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:
   [ b(b(?x_4)) = a(c(c(?x_4))),
     a(c(b(?x_4))) = b(a(c(c(?x_4)))),
     a(c(c(?x))) = b(a(?x)),
     b(a(c(?x_1))) = a(c(b(?x_1))),
     b(a(?x_2)) = a(c(c(?x_2))),
     a(c(a(c(?x_1)))) = b(a(c(b(?x_1)))),
     a(c(a(?x_2))) = b(a(c(c(?x_2)))),
     a(c(b(?x))) = b(a(c(?x))),
     c(b(?x_1)) = b(c(?x_1)),
     c(c(b(?x_1))) = b(c(c(?x_1))),
     b(b(?x_1)) = c(b(c(c(?x_1)))),
     b(b(?x_1)) = c(c(b(c(?x_1)))),
     b(c(b(?x_1))) = c(c(b(c(c(?x_1))))),
     a(b(?x_1)) = b(b(c(?x_1))),
     a(c(b(?x_1))) = b(b(c(c(?x_1)))),
     b(c(?x)) = c(b(?x)),
     b(c(c(?x))) = c(c(b(?x))),
     a(c(c(?x))) = b(b(?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 <b(b(?x_3)), a(c(c(?x_3)))> by Rules <3, 0> preceded by [(b,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 9 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:
   [ b(c(?x)) -> a(?x),
     b(b(?x)) -> a(c(?x)),
     a(?x) -> c(b(?x)),
     c(c(c(?x))) -> b(?x) ]
E-part:
   [ ]
...failed to find a suitable LPO.
unknown Confluence by Ordered Rewriting
Direct Methods: Can't judge

Try Persistent Decomposition for...
   [ b(c(?x)) -> a(?x),
     b(b(?x)) -> a(c(?x)),
     a(?x) -> c(b(?x)),
     c(c(c(?x))) -> b(?x) ]
Sort Assignment:
 a : 11=>11
 b : 11=>11
 c : 11=>11
maximal types: {11}
Persistent Decomposition failed: Can't judge

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

Try Commutative Decomposition for...
   [ b(c(?x)) -> a(?x),
     b(b(?x)) -> a(c(?x)),
     a(?x) -> c(b(?x)),
     c(c(c(?x))) -> b(?x) ]
Inside Critical Pair: <b(b(?x_3)), a(c(c(?x_3)))> by Rules <3, 0>
develop reducts from lhs term...
<{1}, a(c(?x_3))>
<{}, b(b(?x_3))>
develop reducts from rhs term...
<{2}, c(b(c(c(?x_3))))>
<{}, a(c(c(?x_3)))>
Inside Critical Pair: <b(a(?x)), a(c(c(?x)))> by Rules <0, 1>
develop reducts from lhs term...
<{2}, b(c(b(?x)))>
<{}, b(a(?x))>
develop reducts from rhs term...
<{2}, c(b(c(c(?x))))>
<{}, a(c(c(?x)))>
Try A Minimal Decomposition {1,0,3}{2}
{1,0,3}
(cm)Rewrite Rules:
   [ b(b(?x)) -> a(c(?x)),
     b(c(?x)) -> a(?x),
     c(c(c(?x))) -> b(?x) ]
Apply Direct Methods...
Inner CPs:
   [ b(a(?x_1)) = a(c(c(?x_1))),
     b(b(?x_2)) = a(c(c(?x_2))),
     b(a(c(?x))) = a(c(b(?x))),
     c(b(?x)) = b(c(?x)),
     c(c(b(?x))) = b(c(c(?x))) ]
Outer CPs:
   [  ]
not Overlay, check Termination...
Terminating, not WCR
Knuth & Bendix
Direct Methods: not CR
{2}
(cm)Rewrite Rules:
   [ a(?x) -> c(b(?x)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth & Bendix
Direct Methods: CR
Commutative Decomposition failed: Can't judge
No further decomposition possible


Combined result: Can't judge
/tmp/fileie2lfA.trs: Failure(unknown CR)
(1551 msec.)