(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Rewrite Rules:
   [ a -> c,
     a -> h(c,a),
     h(b,f(c)) -> b,
     c -> h(a,h(h(b,a),a)) ]
Apply Direct Methods...
Inner CPs:
   [ h(b,f(h(a,h(h(b,a),a)))) = b ]
Outer CPs:
   [ c = h(c,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:
   [ h(c,a) = c,
     c = h(c,a),
     h(b,f(h(a,h(h(b,a),a)))) = b,
     b = h(b,f(h(a,h(h(b,a),a)))) ]
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(b,f(h(a,h(h(b,a),a)))), b> by Rules <3, 2> preceded by [(h,2),(f,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 (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_{a},q_{b},q_{c},q_{h(h(b,a),a)},q_{h(b,a)}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_{a},
     b -> q_{b},
     c -> q_1,
     c -> q_{a},
     c -> q_{c},
     h(q_{a},q_{h(h(b,a),a)}) -> q_1,
     h(q_{a},q_{h(h(b,a),a)}) -> q_{a},
     h(q_{a},q_{h(h(b,a),a)}) -> q_{c},
     h(q_{b},q_{a}) -> q_{h(b,a)},
     h(q_{c},q_{a}) -> q_0,
     h(q_{c},q_{a}) -> q_{a},
     h(q_{h(b,a)},q_{a}) -> q_{h(h(b,a),a)} ]
Witness for Non-Confluence: <h(c,a), c>
Direct Methods: not CR

Combined result: not CR
668.trs: Success(not CR)
NO
(298 msec.)