(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 -> h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),
     h(h(c,f(f(a))),f(b)) -> a,
     h(c,f(f(c))) -> f(f(a)),
     h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) -> c ]
Apply Direct Methods...
Inner CPs:
   [ h(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(a))),f(b)) = a,
     h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(c))) = f(f(a)),
     h(c,f(f(h(a,h(f(f(f(f(c)))),h(a,h(b,b))))))) = f(f(a)),
     h(f(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) = c,
     h(f(h(c,b)),h(h(h(b,a),h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(h(h(b,a),a)))),c)) = c,
     h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),h(a,h(f(f(f(f(c)))),h(a,h(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:
   [ a = h(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(a))),f(b)),
     f(f(a)) = h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(c))),
     f(f(a)) = h(c,f(f(h(a,h(f(f(f(f(c)))),h(a,h(b,b))))))),
     c = h(f(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)),
     c = h(f(h(c,b)),h(h(h(b,a),h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(h(h(b,a),a)))),c)),
     c = h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))),
     h(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(a))),f(b)) = a,
     h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(h(a,h(f(f(f(f(c)))),h(a,h(b,b))))))) = f(f(a)),
     h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(c))) = f(f(a)),
     h(c,f(f(h(a,h(f(f(f(f(c)))),h(a,h(b,b))))))) = f(f(a)),
     h(f(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),b)),h(h(h(b,a),h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(h(h(b,a),a)))),h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))) = c,
     h(f(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),b)),h(h(h(b,a),h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(h(h(b,a),a)))),c)) = c,
     h(f(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))) = c,
     h(f(h(c,b)),h(h(h(b,a),h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(h(h(b,a),a)))),h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))) = c,
     h(f(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),c)) = c,
     h(f(h(c,b)),h(h(h(b,a),h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(h(h(b,a),a)))),c)) = c,
     h(f(h(c,b)),h(h(h(b,a),h(c,f(h(h(b,a),a)))),h(a,h(f(f(f(f(c)))),h(a,h(b,b)))))) = 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 <h(h(h(a,h(f(f(f(f(c)))),h(a,h(b,b)))),f(f(a))),f(b)), a> by Rules <0, 1> preceded by [(h,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: <h(c,f(f(h(a,h(f(f(f(f(c)))),h(a,h(b,b))))))) <- h(c,f(f(c))) -> f(f(a))>
Direct Methods: not CR

Combined result: not CR
650.trs: Success(not CR)
NO
(73 msec.)