MAYBE
Rewrite Rules:
   [ f(?x,?x) -> a,
     c -> h(c,g(c)),
     h(?x,g(?x)) -> f(?x,h(?x,g(c))) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
not Left-Linear, not Right-Linear
unknown Gomi&Oyamaguchi&Ohta
check Non-Confluence...Unknown
Direct Methods: Can't judge

Try Persistent Decomposition for...
   [ f(?x,?x) -> a,
     c -> h(c,g(c)),
     h(?x,g(?x)) -> f(?x,h(?x,g(c))) ]
Sort Assignment:
 a : =>6
 c : =>6
 f : 6*6=>6
 g : 6=>11
 h : 6*11=>6
maximal types: {6,11}
Persistent Decomposition failed: Can't judge

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

Try Commutative Decomposition for...
   [ f(?x,?x) -> a,
     c -> h(c,g(c)),
     h(?x,g(?x)) -> f(?x,h(?x,g(c))) ]
Commutative Decomposition failed: Can't judge
No further decomposition possible


Final result: Can't judge
24.trs: MAYBE (0 msec.)