(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Rewrite Rules:
   [ c -> a,
     b -> b,
     h(h(b,c),b) -> f(f(h(b,c))),
     h(h(a,f(f(f(a)))),a) -> h(h(f(h(c,h(c,f(b)))),b),c),
     a -> h(h(f(h(b,c)),f(h(a,a))),a) ]
Apply Direct Methods...
Inner CPs:
   [ h(h(b,a),b) = f(f(h(b,c))),
     h(h(b,c),b) = f(f(h(b,c))),
     h(h(b,c),b) = f(f(h(b,c))),
     h(h(h(h(f(h(b,c)),f(h(a,a))),a),f(f(f(a)))),a) = h(h(f(h(c,h(c,f(b)))),b),c),
     h(h(a,f(f(f(h(h(f(h(b,c)),f(h(a,a))),a))))),a) = h(h(f(h(c,h(c,f(b)))),b),c),
     h(h(a,f(f(f(a)))),h(h(f(h(b,c)),f(h(a,a))),a)) = h(h(f(h(c,h(c,f(b)))),b),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(b,c))) = h(h(b,a),b),
     f(f(h(b,c))) = h(h(b,c),b),
     h(h(b,a),b) = f(f(h(b,c))),
     h(h(b,c),b) = f(f(h(b,c))),
     h(h(h(h(f(h(b,c)),f(h(a,a))),a),f(f(f(h(h(f(h(b,c)),f(h(a,a))),a))))),h(h(f(h(b,c)),f(h(a,a))),a)) = h(h(f(h(c,h(c,f(b)))),b),c),
     h(h(h(h(f(h(b,c)),f(h(a,a))),a),f(f(f(h(h(f(h(b,c)),f(h(a,a))),a))))),a) = h(h(f(h(c,h(c,f(b)))),b),c),
     h(h(h(h(f(h(b,c)),f(h(a,a))),a),f(f(f(a)))),h(h(f(h(b,c)),f(h(a,a))),a)) = h(h(f(h(c,h(c,f(b)))),b),c),
     h(h(a,f(f(f(h(h(f(h(b,c)),f(h(a,a))),a))))),h(h(f(h(b,c)),f(h(a,a))),a)) = h(h(f(h(c,h(c,f(b)))),b),c),
     h(h(h(h(f(h(b,c)),f(h(a,a))),a),f(f(f(a)))),a) = h(h(f(h(c,h(c,f(b)))),b),c),
     h(h(a,f(f(f(h(h(f(h(b,c)),f(h(a,a))),a))))),a) = h(h(f(h(c,h(c,f(b)))),b),c),
     h(h(a,f(f(f(a)))),h(h(f(h(b,c)),f(h(a,a))),a)) = h(h(f(h(c,h(c,f(b)))),b),c),
     h(h(f(h(c,h(c,f(b)))),b),c) = h(h(h(h(f(h(b,c)),f(h(a,a))),a),f(f(f(a)))),a),
     h(h(f(h(c,h(c,f(b)))),b),c) = h(h(a,f(f(f(h(h(f(h(b,c)),f(h(a,a))),a))))),a),
     h(h(f(h(c,h(c,f(b)))),b),c) = h(h(a,f(f(f(a)))),h(h(f(h(b,c)),f(h(a,a))),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 <h(h(b,a),b), f(f(h(b,c)))> by Rules <0, 2> preceded by [(h,1),(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 (success)
Witness for Non-Confluence: <h(h(b,h(h(f(h(b,a)),f(h(a,a))),a)),b) <- h(h(b,c),b) -> f(f(h(b,a)))>
Direct Methods: not CR

Combined result: not CR
659.trs: Success(not CR)
NO
(113 msec.)