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

Try Persistent Decomposition for...
   [ f(?x,?x) -> s(s(?x)),
     infty -> s(infty) ]
Sort Assignment:
 f : 8*8=>8
 s : 8=>8
 infty : =>8
maximal types: {8}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ f(?x,?x) -> s(s(?x)),
     infty -> s(infty) ]
Layer Preserving Decomposition failed: Can't judge

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


Final result: Can't judge
example10.trs: MAYBE (0 msec.)