NO
(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Rewrite Rules:
   [ a -> h(a,f(b)),
     f(f(h(a,a))) -> f(f(f(a))),
     f(h(a,h(a,a))) -> f(a),
     f(h(h(b,a),h(f(c),c))) -> c ]
Apply Direct Methods...
Inner CPs:
   [ f(f(h(h(a,f(b)),a))) = f(f(f(a))),
     f(f(h(a,h(a,f(b))))) = f(f(f(a))),
     f(h(h(a,f(b)),h(a,a))) = f(a),
     f(h(a,h(h(a,f(b)),a))) = f(a),
     f(h(a,h(a,h(a,f(b))))) = f(a),
     f(h(h(b,h(a,f(b))),h(f(c),c))) = 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(f(a))) = f(f(h(h(a,f(b)),a))),
     f(f(f(a))) = f(f(h(a,h(a,f(b))))),
     f(a) = f(h(h(a,f(b)),h(a,a))),
     f(a) = f(h(a,h(h(a,f(b)),a))),
     f(a) = f(h(a,h(a,h(a,f(b))))),
     c = f(h(h(b,h(a,f(b))),h(f(c),c))),
     f(f(h(h(a,f(b)),h(a,f(b))))) = f(f(f(a))),
     f(f(h(h(a,f(b)),a))) = f(f(f(a))),
     f(f(h(a,h(a,f(b))))) = f(f(f(a))),
     f(h(h(a,f(b)),h(h(a,f(b)),h(a,f(b))))) = f(a),
     f(h(h(a,f(b)),h(h(a,f(b)),a))) = f(a),
     f(h(h(a,f(b)),h(a,h(a,f(b))))) = f(a),
     f(h(a,h(h(a,f(b)),h(a,f(b))))) = f(a),
     f(h(h(a,f(b)),h(a,a))) = f(a),
     f(h(a,h(h(a,f(b)),a))) = f(a),
     f(h(a,h(a,h(a,f(b))))) = f(a),
     f(h(h(b,h(a,f(b))),h(f(c),c))) = 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(h(a,f(b)),a))), f(f(f(a)))> by Rules <0, 1> preceded by [(f,1),(f,1),(h,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(h(h(b,h(a,f(b))),h(f(c),c))) <- f(h(h(b,a),h(f(c),c))) -> c>
Direct Methods: not CR

Combined result: not CR
716.trs: Success(not CR)
(5 msec.)