(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(c) -> a,
     f(a) -> c,
     c -> f(h(a,h(f(c),c))),
     h(f(c),f(b)) -> f(h(a,c)) ]
Apply Direct Methods...
Inner CPs:
   [ f(f(h(a,h(f(c),c)))) = a,
     h(a,f(b)) = f(h(a,c)),
     h(f(f(h(a,h(f(c),c)))),f(b)) = f(h(a,c)) ]
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(f(h(a,h(f(c),c)))) = a,
     f(h(a,c)) = h(a,f(b)),
     a = f(f(h(a,h(f(c),c)))),
     f(h(a,c)) = h(f(f(h(a,h(f(c),c)))),f(b)),
     h(a,f(b)) = f(h(a,c)),
     h(f(f(h(a,h(f(c),c)))),f(b)) = f(h(a,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(f(h(a,h(f(c),c)))), a> by Rules <2, 0> preceded by [(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 12 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(h(a,c)) <- h(f(c),f(b)) -> h(a,f(b))>
Direct Methods: not CR

Combined result: not CR
663.trs: Success(not CR)
NO
(65 msec.)