(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Rewrite Rules:
   [ f(h(b,c)) -> c,
     a -> h(h(h(f(a),b),h(c,c)),f(b)),
     h(f(a),a) -> h(c,a),
     b -> b,
     h(h(b,f(b)),h(a,c)) -> b ]
Apply Direct Methods...
Inner CPs:
   [ f(h(b,c)) = c,
     h(f(h(h(h(f(a),b),h(c,c)),f(b))),a) = h(c,a),
     h(f(a),h(h(h(f(a),b),h(c,c)),f(b))) = h(c,a),
     h(h(b,f(b)),h(h(h(h(f(a),b),h(c,c)),f(b)),c)) = b,
     h(h(b,f(b)),h(a,c)) = b,
     h(h(b,f(b)),h(a,c)) = b ]
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(h(b,c)) = c,
     h(c,a) = h(f(h(h(h(f(a),b),h(c,c)),f(b))),a),
     h(c,a) = h(f(a),h(h(h(f(a),b),h(c,c)),f(b))),
     b = h(h(b,f(b)),h(h(h(h(f(a),b),h(c,c)),f(b)),c)),
     h(f(h(h(h(f(a),b),h(c,c)),f(b))),h(h(h(f(a),b),h(c,c)),f(b))) = h(c,a),
     h(f(h(h(h(f(a),b),h(c,c)),f(b))),a) = h(c,a),
     h(f(a),h(h(h(f(a),b),h(c,c)),f(b))) = h(c,a),
     c = f(h(b,c)),
     b = h(h(b,f(b)),h(a,c)),
     h(h(b,f(b)),h(h(h(h(f(a),b),h(c,c)),f(b)),c)) = b,
     h(h(b,f(b)),h(a,c)) = b ]
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(h(b,c)), c> by Rules <3, 0> preceded by [(f,1),(h,1)]
 joinable by a reduction of rules <[([],0)], []>
Critical Pair <h(f(h(h(h(f(a),b),h(c,c)),f(b))),a), h(c,a)> by Rules <1, 2> preceded by [(h,1),(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 75 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <h(f(h(h(h(f(a),b),h(c,c)),f(b))),a) <- h(f(a),a) -> h(c,a)>
Direct Methods: not CR

Combined result: not CR
701.trs: Success(not CR)
NO
(22 msec.)