(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Rewrite Rules:
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]
Apply Direct Methods...
Inner CPs:
   [ f(h(f(c),c)) = a,
     f(h(c,f(c))) = a ]
Outer CPs:
   [  ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
inner CP cond (upside-parallel)
innter CP Cond (outside)
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ f(h(f(c),f(c))) = a,
     f(h(f(c),c)) = a,
     f(h(c,f(c))) = a,
     a = f(h(f(c),c)),
     a = f(h(c,f(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(f(c),c)), a> by Rules <3, 0> preceded by [(f,1),(h,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 75 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),(b,0),(c,0),(f,1),(h,2)}
   Q = {q_0,q_1,q_{c},q_{f(c)},q_{h(c,f(c))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_1,
     b -> q_1,
     c -> q_{c},
     f(q_{c}) -> q_{c},
     f(q_{c}) -> q_{f(c)},
     f(q_{h(c,f(c))}) -> q_0,
     h(q_{c},q_{f(c)}) -> q_{h(c,f(c))} ]
Witness for Non-Confluence: <f(h(c,f(c))), a>
Direct Methods: not CR

Combined result: not CR
706.trs: Success(not CR)
NO
(136 msec.)