NO
(ignored inputs)COMMENT from the collection of \cite{Aoto2013}
Rewrite Rules:
   [ a(?x) -> b(b(b(?x))),
     a(?x) -> c(?x),
     b(?x) -> b(?x) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ b(b(b(?x))) = c(?x) ]
Overlay, check Innermost Termination...
unknown Innermost 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:
   [ c(?x) = b(b(b(?x))),
     b(b(b(?x))) = 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 <c(?x_1), b(b(b(?x_1)))> by Rules <1, 0> preceded by []
unknown Diagram Decreasing
check Non-Confluence...
obtain 13 rules by 3 steps unfolding
strenghten b(b(b(?x_1))) and c(?x_1)
obtain 1 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Root-Approximation (success)
Witness for Non-Confluence: <b(b(b(c_1))), c(c_1)>
Direct Methods: not CR

Final result: not CR
236.trs: Success(not CR)
(8 msec.)