(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(f(b),a)) -> b,
     f(c) -> b,
     b -> f(b) ]
Apply Direct Methods...
Inner CPs:
   [ f(h(f(f(b)),a)) = b ]
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(f(b)),a)) = b,
     b = f(h(f(f(b)),a)) ]
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(f(b)),a)), b> by Rules <2, 0> preceded by [(f,1),(h,1),(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 11 rules by 3 steps unfolding
obtain 66 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_{h(f(f(b)),a)},q_{a},q_{b},q_{f(b)},q_{f(f(b))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_{a},
     b -> q_1,
     b -> q_{b},
     f(q_1) -> q_1,
     f(q_1) -> q_{b},
     f(q_{h(f(f(b)),a)}) -> q_0,
     f(q_{b}) -> q_{f(b)},
     f(q_{f(b)}) -> q_{f(f(b))},
     h(q_{f(f(b))},q_{a}) -> q_{h(f(f(b)),a)} ]
Witness for Non-Confluence: <f(h(f(f(b)),a)), b>
Direct Methods: not CR

Combined result: not CR
711.trs: Success(not CR)
NO
(234 msec.)