NO
(ignored inputs)COMMENT from the collection of \cite{Aoto2013}
Rewrite Rules:
   [ a(?x) -> g(g(b(?x))),
     a(?x) -> g(c(?x)),
     b(?x) -> g(b(?x)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ g(g(b(?x))) = g(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:
   [ g(c(?x)) = g(g(b(?x))),
     g(g(b(?x))) = g(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 <g(c(?x_1)), g(g(b(?x_1)))> by Rules <1, 0> preceded by []
unknown Diagram Decreasing
check Non-Confluence...
obtain 13 rules by 3 steps unfolding
strenghten g(g(b(?x_1))) and g(c(?x_1))
strenghten g(g(b(?x_6))) and g(b(?x_6))
strenghten g(g(g(b(?x_7)))) and g(c(?x_7))
strenghten g(g(g(b(?x_8)))) and g(b(?x_8))
strenghten g(c(g(b(?x_2)))) and a(g(b(?x_2)))
strenghten g(c(g(b(?x_12)))) and g(c(b(?x_12)))
strenghten g(c(g(c(?x_1)))) and a(g(c(?x_1)))
strenghten g(c(g(c(?x_11)))) and g(c(a(?x_11)))
strenghten g(g(g(b(?x_7)))) and g(g(b(?x_7)))
strenghten g(g(g(g(b(?x_9))))) and g(c(?x_9))
strenghten g(g(g(g(b(?x_10))))) and g(b(?x_10))
strenghten g(c(g(b(?x_6)))) and a(g(g(b(?x_6))))
strenghten g(c(g(c(?x)))) and a(g(g(b(?x))))
strenghten g(g(b(a(?x_11)))) and g(c(g(c(?x_11))))
strenghten g(g(b(b(?x_12)))) and g(c(g(b(?x_12))))
strenghten g(g(g(g(b(?x_9))))) and g(g(b(?x_9)))
strenghten a(g(g(g(b(?x_7))))) and g(c(g(c(?x_7))))
strenghten a(g(g(g(b(?x_8))))) and g(c(g(b(?x_8))))
strenghten g(g(g(b(a(?x_11))))) and g(c(g(c(?x_11))))
strenghten g(g(g(b(b(?x_12))))) and g(c(g(b(?x_12))))
strenghten g(g(g(g(b(?x_9))))) and g(g(g(b(?x_9))))
strenghten g(c(g(c(a(?x))))) and a(g(c(g(c(?x)))))
strenghten g(c(g(c(b(?x_12))))) and a(g(c(g(b(?x_12)))))
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <g(g(b(c_1))), g(c(c_1))>
Direct Methods: not CR

Final result: not CR
238.trs: Success(not CR)
(17 msec.)