MAYBE
Rewrite Rules:
   [ f(?x,?x) -> h(?x,?x),
     f(g(?x),?x) -> a,
     c -> g(c),
     h(g(?x),?x) -> a ]
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) -> h(?x,?x),
     f(g(?x),?x) -> a,
     c -> g(c),
     h(g(?x),?x) -> a ]
Sort Assignment:
 a : =>14
 c : =>15
 f : 15*15=>14
 g : 15=>15
 h : 15*15=>14
maximal types: {14,15}
Persistent Decomposition failed: Can't judge

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

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


Final result: Can't judge
27.trs: MAYBE (4 msec.)