NO
(ignored inputs)COMMENT reduction failed
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)
 (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
<F,Q,Q_f,Delta> where
   F = {(a,0),(b,0),(c,0),(f,1),(h,2)}
   Q = {q_0,q_1,q_{h(a,f(c))},q_{h(a,h(b,h(f(b),b)))},q_{f(h(a,h(b,h(f(b),b))))},q_{a},q_{b},q_{c},q_{f(b)},q_{f(c)},q_{h(b,h(f(b),b))},q_{h(f(b),b)}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_1,
     a -> q_{a},
     b -> q_{b},
     c -> q_{c},
     f(q_{h(a,h(b,h(f(b),b)))}) -> q_{f(h(a,h(b,h(f(b),b))))},
     f(q_{f(h(a,h(b,h(f(b),b))))}) -> q_0,
     f(q_{b}) -> q_{f(b)},
     f(q_{c}) -> q_{f(c)},
     h(q_{a},q_{f(c)}) -> q_{h(a,f(c))},
     h(q_{a},q_{h(b,h(f(b),b))}) -> q_{h(a,h(b,h(f(b),b)))},
     h(q_{b},q_{h(f(b),b)}) -> q_{h(b,h(f(b),b))},
     h(q_{f(b)},q_{b}) -> q_{b},
     h(q_{f(b)},q_{b}) -> q_{h(f(b),b)},
     h(q_{f(c)},q_{h(a,f(c))}) -> q_1,
     h(q_{f(c)},q_{h(a,f(c))}) -> q_{a} ]
 (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly)Witness for Non-Confluence: <f(f(h(a,h(b,b)))) <- f(f(h(a,h(b,b)))) -> a>
Direct Methods: not CR

Combined result: not CR
/tmp/fileSzCkJB.trs: Success(not CR)
(912 msec.)