NO
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ a -> f(c),
     a -> h(c),
     f(?x) -> h(g(?x)),
     h(?x) -> f(g(?x)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ f(c) = h(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(c) = f(c),
     f(c) = h(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(c), f(c)> by Rules <1, 0> preceded by []
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 96 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (success)
Polynomial Interpretation:
  c:= (1)
  f:= (1)+(1)*x1
  g:= (1)+(1)*x1
  h:= (1)*x1
 [h(?x)]-[f(g(?x))] = (~2) = 0 (mod 2)
 [f(?x)]-[h(g(?x))] = 0 = 0 (mod 2)
 [h(g(?x))]-[f(?x)] = 0 = 0 (mod 2)
 [f(g(?x))]-[h(?x)] = (2) = 0 (mod 2)
 [f(c)]-[h(c)] = (1) = 1 (mod 2)
 (success)
Witness for Non-Confluence: <f(c) <- a -> h(c)>
Direct Methods: not CR

Combined result: not CR
/tmp/file6pzbBq.trs: Success(not CR)
(519 msec.)