(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 -> a,
     f(c) -> f(h(b,c)),
     a -> c,
     c -> h(f(c),h(b,h(h(b,c),a))),
     c -> b ]
Apply Direct Methods...
Inner CPs:
   [ f(a) = f(h(b,c)),
     f(h(f(c),h(b,h(h(b,c),a)))) = f(h(b,c)),
     f(b) = f(h(b,c)) ]
Outer CPs:
   [ a = h(f(c),h(b,h(h(b,c),a))),
     a = b,
     h(f(c),h(b,h(h(b,c),a))) = b ]
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:
   [ h(f(c),h(b,h(h(b,c),a))) = a,
     b = a,
     f(h(b,c)) = f(a),
     f(a) = f(h(b,c)),
     f(h(f(c),h(b,h(h(b,c),a)))) = f(h(b,c)),
     f(b) = f(h(b,c)),
     a = h(f(c),h(b,h(h(b,c),a))),
     b = h(f(c),h(b,h(h(b,c),a))),
     f(h(b,c)) = f(h(f(c),h(b,h(h(b,c),a)))),
     a = b,
     h(f(c),h(b,h(h(b,c),a))) = b,
     f(h(b,c)) = f(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(a), f(h(b,c))> by Rules <0, 1> preceded by [(f,1)]
 joinable by a reduction of rules <[([(f,1)],2),([],1)], []>
Critical Pair <f(h(f(c),h(b,h(h(b,c),a)))), f(h(b,c))> by Rules <3, 1> preceded by [(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 12 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(h(b,a)) <- f(c) -> f(b)>
Direct Methods: not CR

Combined result: not CR
712.trs: Success(not CR)
NO
(35548 msec.)