(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 -> f(f(c)),
     h(h(h(b,b),f(f(a))),f(f(f(a)))) -> a,
     b -> h(h(f(a),c),f(a)) ]
Apply Direct Methods...
Inner CPs:
   [ h(h(h(h(h(f(a),c),f(a)),b),f(f(a))),f(f(f(a)))) = a,
     h(h(h(b,h(h(f(a),c),f(a))),f(f(a))),f(f(f(a)))) = a ]
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:
   [ h(h(h(h(h(f(a),c),f(a)),h(h(f(a),c),f(a))),f(f(a))),f(f(f(a)))) = a,
     h(h(h(h(h(f(a),c),f(a)),b),f(f(a))),f(f(f(a)))) = a,
     h(h(h(b,h(h(f(a),c),f(a))),f(f(a))),f(f(f(a)))) = a,
     a = h(h(h(h(h(f(a),c),f(a)),b),f(f(a))),f(f(f(a)))),
     a = h(h(h(b,h(h(f(a),c),f(a))),f(f(a))),f(f(f(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(h(h(h(f(a),c),f(a)),b),f(f(a))),f(f(f(a)))), a> by Rules <2, 1> preceded by [(h,1),(h,1),(h,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 84 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <h(h(h(b,h(h(f(a),c),f(a))),f(f(a))),f(f(f(a)))) <- h(h(h(b,b),f(f(a))),f(f(f(a)))) -> a>
Direct Methods: not CR

Combined result: not CR
676.trs: Success(not CR)
NO
(55 msec.)