NO
(ignored inputs)COMMENT from the collection of \cite{Aoto2013}
Rewrite Rules:
   [ a(?x) -> b(?x),
     a(?x) -> c(c(?x)),
     b(?x) -> g(b(?x)),
     c(?x) -> c(?x) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ b(?x) = c(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(c(?x)) = b(?x),
     b(?x) = 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 <c(c(?x_1)), b(?x_1)> by Rules <1, 0> preceded by []
unknown Diagram Decreasing
check Non-Confluence...
obtain 14 rules by 3 steps unfolding
strenghten c(c(?x_1)) and b(?x_1)
strenghten g(b(?x_7)) and b(?x_7)
strenghten c(c(?x_7)) and g(b(?x_7))
strenghten g(b(?x_8)) and c(c(?x_8))
obtain 16 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Root-Approximation (success)
Witness for Non-Confluence: <c(c(c_1)), b(c_1)>
Direct Methods: not CR

Final result: not CR
240.trs: Success(not CR)
(15 msec.)