(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
Rewrite Rules:
   [ h(h(c,a),b) -> b,
     a -> h(a,b),
     a -> a ]
Apply Direct Methods...
Inner CPs:
   [ h(h(c,h(a,b)),b) = b,
     h(h(c,a),b) = b ]
Outer CPs:
   [ h(a,b) = 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
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(h(c,h(a,b)),b) = b,
     h(h(c,a),b) = b,
     a = h(a,b),
     b = h(h(c,h(a,b)),b),
     h(a,b) = a,
     b = h(h(c,a),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 <h(h(c,h(a,b)),b), b> by Rules <1, 0> preceded by [(h,1),(h,2)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 51 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),(h,2)}
   Q = {q_0,q_1,q_{a},q_{b},q_{c},q_{h(a,b)},q_{h(c,h(a,b))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_{a},
     b -> q_1,
     b -> q_{b},
     c -> q_{c},
     h(q_{a},q_{b}) -> q_{a},
     h(q_{a},q_{b}) -> q_{h(a,b)},
     h(q_{c},q_{h(a,b)}) -> q_{h(c,h(a,b))},
     h(q_{h(c,h(a,b))},q_{b}) -> q_0 ]
Witness for Non-Confluence: <h(h(c,h(a,b)),b), b>
Direct Methods: not CR

Combined result: not CR
697.trs: Success(not CR)
NO
(89 msec.)