(ignored inputs)COMMENT from experiments for [44] submitted by: Tsubasa Suzuki , Takahito Aoto , and Yoshihito Toyama
Rewrite Rules:
   [ a -> f(c),
     a -> f(h(c)),
     f(?x) -> h(f(?x)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ f(c) = f(h(c)) ]
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:
   [ f(h(c)) = f(c),
     f(c) = f(h(c)) ]
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 <f(h(c)), f(c)> by Rules <1, 0> preceded by []
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 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 (success)
<F,Q,Q_f,Delta> where
   F = {(a,0),(c,0),(f,1),(h,1)}
   Q = {q_0,q_1,q_{c},q_{h(c)}}
   Qf = {q_0,q_1}
   Delta = 
   [ c -> q_{c},
     f(q_{c}) -> q_1,
     f(q_{h(c)}) -> q_0,
     h(q_0) -> q_0,
     h(q_1) -> q_1,
     h(q_{c}) -> q_{h(c)} ]
Witness for Non-Confluence: <f(h(c)), f(c)>
Direct Methods: not CR

Combined result: not CR
254.trs: Success(not CR)
NO
(21 msec.)