(ignored inputs)COMMENT Example 3 of \cite{Toy98}
Rewrite Rules:
   [ a(f(?x),?y) -> f(a(f(?y),?x)),
     a(b(?x),?y) -> a(?x,b(?x)),
     a(g(?x),?x) -> g(b(g(?x))) ]
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...
   [ a(f(?x),?y) -> f(a(f(?y),?x)),
     a(b(?x),?y) -> a(?x,b(?x)),
     a(g(?x),?x) -> g(b(g(?x))) ]
Sort Assignment:
 a : 15*15=>15
 b : 15=>15
 f : 15=>15
 g : 15=>15
maximal types: {15}
Persistent Decomposition failed: Can't judge

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

Try Commutative Decomposition for...
   [ a(f(?x),?y) -> f(a(f(?y),?x)),
     a(b(?x),?y) -> a(?x,b(?x)),
     a(g(?x),?x) -> g(b(g(?x))) ]
Commutative Decomposition failed (not left-linear): Can't judge
No further decomposition possible


Final result: Can't judge
/local-scratch/hzankl/2012/cops2012/91.trs: Failure(unknown)
(1 msec.)