MAYBE
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]
Apply Direct Methods...
Inner CPs:
   [ f(h(f(c),c)) = a,
     f(h(c,f(c))) = a ]
Outer CPs:
   [  ]
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:
   [ f(h(f(c),f(c))) = a,
     f(h(f(c),c)) = a,
     f(h(c,f(c))) = a,
     a = f(h(f(c),c)),
     a = f(h(c,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 <f(h(f(c),c)), a> by Rules <3, 0> preceded by [(f,1),(h,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 75 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_{c},q_{f(c)},q_{h(c,f(c))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_1,
     b -> q_1,
     c -> q_{c},
     f(q_{c}) -> q_{c},
     f(q_{c}) -> q_{f(c)},
     f(q_{h(c,f(c))}) -> q_0,
     h(q_{c},q_{f(c)}) -> q_{h(c,f(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:
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]
E-part:
   [ ]
...failed to find a suitable LPO.
unknown Confluence by Ordered Rewriting
Direct Methods: Can't judge

Try Persistent Decomposition for...
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]
Sort Assignment:
 a : =>9
 b : =>9
 c : =>9
 f : 9=>9
 h : 9*9=>9
maximal types: {9}
Persistent Decomposition failed: Can't judge

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

Try Commutative Decomposition for...
   [ f(h(c,c)) -> a,
     a -> b,
     f(b) -> f(c),
     c -> f(c) ]
Inside Critical Pair: <f(h(f(c),c)), a> by Rules <3, 0>
develop reducts from lhs term...
<{3}, f(h(f(f(c)),f(c)))>
<{3}, f(h(f(f(c)),c))>
<{3}, f(h(f(c),f(c)))>
<{}, f(h(f(c),c))>
develop reducts from rhs term...
<{1}, b>
<{}, a>
Inside Critical Pair: <f(h(c,f(c))), a> by Rules <3, 0>
develop reducts from lhs term...
<{3}, f(h(f(c),f(f(c))))>
<{3}, f(h(f(c),f(c)))>
<{3}, f(h(c,f(f(c))))>
<{}, f(h(c,f(c)))>
develop reducts from rhs term...
<{1}, b>
<{}, a>
Try A Minimal Decomposition {0,3}{1}{2}
{0,3}
(cm)Rewrite Rules:
   [ f(h(c,c)) -> a,
     c -> f(c) ]
Apply Direct Methods...
Inner CPs:
   [ f(h(f(c),c)) = a,
     f(h(c,f(c))) = a ]
Outer CPs:
   [  ]
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:
   [ f(h(f(c),f(c))) = a,
     f(h(f(c),c)) = a,
     f(h(c,f(c))) = a,
     a = f(h(f(c),c)),
     a = f(h(c,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 <f(h(f(c),c)), a> by Rules <1, 0> preceded by [(f,1),(h,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 10 rules by 3 steps unfolding
obtain 79 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,2)}
   Q = {q_0,q_1,q_{c},q_{f(c)},q_{h(c,f(c))}}
   Qf = {q_0,q_1}
   Delta = 
   [ a -> q_1,
     c -> q_{c},
     f(q_{c}) -> q_{c},
     f(q_{c}) -> q_{f(c)},
     f(q_{h(c,f(c))}) -> q_0,
     h(q_{c},q_{f(c)}) -> q_{h(c,f(c))} ]
 (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (success)
Polynomial Interpretation:
  a:= (8)
  c:= (1)
  f:= (3)+(1)*x1
  h:= (2)+(1)*x2
 [f(c)]-[c] = (3) >= 0
 [a]-[f(h(c,c))] = (2) >= 0
 [f(h(c,f(c)))]-[a] = (1) > 0
 (success)
Witness for Non-Confluence: <f(h(c,f(c))) <- f(h(c,c)) -> a>
Direct Methods: not CR
{1}
(cm)Rewrite Rules:
   [ a -> b ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth & Bendix
Direct Methods: CR
{2}
(cm)Rewrite Rules:
   [ f(b) -> f(c) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth & Bendix
Direct Methods: CR
Commutative Decomposition failed: Can't judge
No further decomposition possible


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