(ignored inputs)COMMENT due to Barendregt , from p.813 of \cite{Hue80}
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
unknown Knuth&Bendix
not Left-Linear, not Right-Linear
unknown Strongly Depth-Preserving & Non-E-Overlapping
check by Reduction-Preserving Completion...
failure(empty P)
unknown Reduction-Preserving Completion
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 (not left-linear): Can't judge
No further decomposition possible


Final result: Can't judge
/local-scratch/hzankl/2012/cops2012/47.trs: Failure(unknown)
(0 msec.)