MAYBE
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ a -> f(c),
     a -> f(h(c)),
     f(?x) -> h(f(?x)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ f(c) = f(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:
   [ f(h(c)) = f(c),
     f(c) = f(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 <f(h(c)), f(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)
<F,Q,Q_f,Delta> where
   F = {(a,0),(c,0),(f,1),(h,1)}
   Q = {q_0,q_1,q_{c},q_{h(c)}}
   Qf = {q_0,q_1}
   Delta = 
   [ c -> q_{c},
     f(q_{c}) -> q_1,
     f(q_{h(c)}) -> q_0,
     h(q_0) -> q_0,
     h(q_1) -> q_1,
     h(q_{c}) -> q_{h(c)} ]
 (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
unknown Non-Confluence
unknown Huet (modulo AC)
check by Reduction-Preserving Completion...
failure(empty P)
unknown Reduction-Preserving Completion
check by Ordered Rewriting...
remove redundants rules and split
R-part:
   [ a -> f(c),
     a -> f(h(c)),
     f(?x) -> h(f(?x)) ]
E-part:
   [ ]
...failed to find a suitable LPO.
unknown Confluence by Ordered Rewriting
Direct Methods: Can't judge

Try Persistent Decomposition for...
   [ a -> f(c),
     a -> f(h(c)),
     f(?x) -> h(f(?x)) ]
Sort Assignment:
 a : =>8
 c : =>8
 f : 8=>8
 h : 8=>8
maximal types: {8}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ a -> f(c),
     a -> f(h(c)),
     f(?x) -> h(f(?x)) ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ a -> f(c),
     a -> f(h(c)),
     f(?x) -> h(f(?x)) ]
Outside Critical Pair: <f(h(c)), f(c)> by Rules <1, 0>
develop reducts from lhs term...
<{2}, h(f(h(c)))>
<{}, f(h(c))>
develop reducts from rhs term...
<{2}, h(f(c))>
<{}, f(c)>
Try A Minimal Decomposition {0,1}{2}
{0,1}
(cm)Rewrite Rules:
   [ a -> f(c),
     a -> f(h(c)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ f(c) = f(h(c)) ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), not WCR
Knuth & Bendix
Direct Methods: not CR
{2}
(cm)Rewrite Rules:
   [ f(?x) -> h(f(?x)) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
unknown Knuth & Bendix
Linear
Development Closed
Direct Methods: CR
Commutative Decomposition failed: Can't judge
No further decomposition possible


Combined result: Can't judge
/tmp/filehNBkJq.trs: Failure(unknown CR)
(341 msec.)