(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Rewrite Rules:
   [ b -> b,
     a -> h(f(c),h(a,f(c))),
     f(f(h(a,h(b,b)))) -> a,
     h(c,c) -> b,
     b -> h(f(b),b) ]
Apply Direct Methods...
Inner CPs:
   [ f(f(h(a,h(b,b)))) = a,
     f(f(h(a,h(b,b)))) = a,
     f(f(h(h(f(c),h(a,f(c))),h(b,b)))) = a,
     f(f(h(a,h(h(f(b),b),b)))) = a,
     f(f(h(a,h(b,h(f(b),b))))) = a ]
Outer CPs:
   [ b = h(f(b),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
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(f(b),b) = b,
     a = f(f(h(a,h(b,b)))),
     a = f(f(h(h(f(c),h(a,f(c))),h(b,b)))),
     f(f(h(h(f(c),h(a,f(c))),h(b,b)))) = a,
     f(f(h(h(f(c),h(a,f(c))),h(b,h(f(b),b))))) = a,
     f(f(h(h(f(c),h(a,f(c))),h(h(f(b),b),b)))) = a,
     f(f(h(h(f(c),h(a,f(c))),h(h(f(b),b),h(f(b),b))))) = a,
     f(f(h(a,h(b,b)))) = a,
     f(f(h(a,h(b,h(f(b),b))))) = a,
     f(f(h(a,h(h(f(b),b),b)))) = a,
     f(f(h(a,h(h(f(b),b),h(f(b),b))))) = a,
     b = h(f(b),b),
     a = f(f(h(a,h(h(f(b),b),b)))),
     a = f(f(h(a,h(b,h(f(b),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(f(h(a,h(b,b)))), a> by Rules <0, 2> preceded by [(f,1),(f,1),(h,2),(h,1)]
 joinable by a reduction of rules <[([],2)], []>
Critical Pair <f(f(h(a,h(b,b)))), a> by Rules <0, 2> preceded by [(f,1),(f,1),(h,2),(h,2)]
 joinable by a reduction of rules <[([],2)], []>
Critical Pair <f(f(h(h(f(c),h(a,f(c))),h(b,b)))), a> by Rules <1, 2> preceded by [(f,1),(f,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: <f(f(h(h(f(c),h(a,f(c))),h(b,b)))) <- f(f(h(a,h(b,b)))) -> h(f(c),h(a,f(c)))>
Direct Methods: not CR

Combined result: not CR
666.trs: Success(not CR)
NO
(69 msec.)