NO
(ignored inputs)COMMENT Example 17 of \cite{Aoto2013} COMMENT from the collection of \cite{Aoto2013}
Rewrite Rules:
   [ c -> f(c,d),
     c -> h(c,d),
     f(?x,?y) -> h(g(?y),?x),
     h(?x,?y) -> f(g(?y),?x) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ f(c,d) = h(c,d) ]
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:
   [ h(c,d) = f(c,d),
     f(c,d) = h(c,d) ]
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 <h(c,d), f(c,d)> by Rules <1, 0> preceded by []
unknown Diagram Decreasing
check Non-Confluence...
obtain 14 rules by 3 steps unfolding
strenghten f(c,d) and h(c,d)
strenghten h(c,d) and f(c,d)
strenghten f(g(d),c) and f(c,d)
strenghten f(g(d),c) and h(c,d)
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Root-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Precedence:
 c : Mul [];
 h : Mul [1],  f : Mul [2],  d : Mul [];
 g : !1;
Obtained:
 h(f(d)) :(gt): f(d)
 (c -> f(c,d): not usable)
 (c -> h(c,d): not usable)
 f(?y) :(ge): h(?y)
 h(?x) :(ge): f(?x)
Witness for Non-Confluence: <h(f(c,d),d), f(c,d)>
Direct Methods: not CR

Final result: not CR
257.trs: Success(not CR)
(1194 msec.)