(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Rewrite Rules:
   [ h(f(b),a) -> h(f(h(c,a)),f(a)),
     c -> f(c),
     c -> h(f(b),c),
     a -> c,
     f(a) -> b ]
Apply Direct Methods...
Inner CPs:
   [ h(f(b),c) = h(f(h(c,a)),f(a)),
     f(c) = b ]
Outer CPs:
   [ f(c) = h(f(b),c) ]
not Overlay, check Termination...
unknown/not 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(f(b),c) = h(f(h(c,a)),f(a)),
     h(f(b),c) = f(c),
     f(c) = h(f(b),c),
     h(f(h(c,a)),f(a)) = h(f(b),c),
     b = f(c),
     f(c) = b ]
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(f(b),c), h(f(h(c,a)),f(a))> by Rules <3, 0> preceded by [(h,2)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 11 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)
Witness for Non-Confluence: <f(c) <- f(a) -> b>
Direct Methods: not CR

Combined result: not CR
657.trs: Success(not CR)
NO
(89 msec.)