(ignored inputs)COMMENT doi:10.1007/978-3-642-40885-4_22 [44] Example 8 submitted by: Tsubasa Suzuki , Takahito Aoto , and Yoshihito Toyama
Rewrite Rules:
   [ a -> h(c),
     a -> h(f(c)),
     h(?x) -> h(h(?x)),
     f(?x) -> f(g(?x)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ h(c) = h(f(c)) ]
Overlay, check Innermost Termination...
unknown Innermost 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(c),
     h(c) = h(f(c)) ]
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(f(c)), h(c)> by Rules <1, 0> preceded by []
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 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)
Witness for Non-Confluence: <h(f(c)) <- a -> h(c)>
Direct Methods: not CR

Combined result: not CR
245.trs: Success(not CR)
NO
(40 msec.)