MAYBE
Rewrite Rules:
   [ F(?x,?x) -> A,
     G(?x) -> F(?x,G(?x)),
     C -> 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,
     G(?x) -> F(?x,G(?x)),
     C -> G(C) ]
Sort Assignment:
 A : =>10
 C : =>10
 F : 10*10=>10
 G : 10=>10
maximal types: {10}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ F(?x,?x) -> A,
     G(?x) -> F(?x,G(?x)),
     C -> G(C) ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ F(?x,?x) -> A,
     G(?x) -> F(?x,G(?x)),
     C -> G(C) ]
Commutative Decomposition failed: Can't judge
No further decomposition possible


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