(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 -> c,
     b -> f(c),
     h(b,h(a,f(h(a,f(f(f(b))))))) -> h(a,f(a)),
     b -> h(b,a),
     h(f(b),c) -> f(c) ]
Apply Direct Methods...
Inner CPs:
   [ h(f(c),h(a,f(h(a,f(f(f(b))))))) = h(a,f(a)),
     h(b,h(a,f(h(a,f(f(f(f(c)))))))) = h(a,f(a)),
     h(h(b,a),h(a,f(h(a,f(f(f(b))))))) = h(a,f(a)),
     h(b,h(a,f(h(a,f(f(f(h(b,a)))))))) = h(a,f(a)),
     h(f(b),c) = f(c),
     h(f(f(c)),c) = f(c),
     h(f(h(b,a)),c) = f(c) ]
Outer CPs:
   [ f(c) = h(b,a) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ f(c) = h(f(b),c),
     h(b,a) = f(c),
     h(a,f(a)) = h(f(c),h(a,f(h(a,f(f(f(b))))))),
     h(a,f(a)) = h(b,h(a,f(h(a,f(f(f(f(c)))))))),
     f(c) = h(f(f(c)),c),
     h(f(c),h(a,f(h(a,f(f(f(f(c)))))))) = h(a,f(a)),
     h(f(c),h(a,f(h(a,f(f(f(h(b,a)))))))) = h(a,f(a)),
     h(h(b,a),h(a,f(h(a,f(f(f(f(c)))))))) = h(a,f(a)),
     h(h(b,a),h(a,f(h(a,f(f(f(h(b,a)))))))) = h(a,f(a)),
     h(f(c),h(a,f(h(a,f(f(f(b))))))) = h(a,f(a)),
     h(h(b,a),h(a,f(h(a,f(f(f(b))))))) = h(a,f(a)),
     h(b,h(a,f(h(a,f(f(f(f(c)))))))) = h(a,f(a)),
     h(b,h(a,f(h(a,f(f(f(h(b,a)))))))) = h(a,f(a)),
     f(c) = h(b,a),
     h(a,f(a)) = h(h(b,a),h(a,f(h(a,f(f(f(b))))))),
     h(a,f(a)) = h(b,h(a,f(h(a,f(f(f(h(b,a)))))))),
     f(c) = h(f(h(b,a)),c),
     h(f(f(c)),c) = f(c),
     h(f(h(b,a)),c) = f(c),
     h(f(b),c) = f(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(f(c),h(a,f(h(a,f(f(f(b))))))), h(a,f(a))> by Rules <1, 2> preceded by [(h,1)]
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(b,a) <- b -> f(c)>
Direct Methods: not CR

Combined result: not CR
715.trs: Success(not CR)
NO
(16 msec.)