(ignored inputs)COMMENT Example 5.9 from [MH94]
Rewrite Rules:
   [ f(?x) -> g(?x,h(?x)),
     g(?x,?x) -> a,
     b -> h(b) ]
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) -> g(?x,h(?x)),
     g(?x,?x) -> a,
     b -> h(b) ]
Sort Assignment:
 a : =>13
 b : =>12
 f : 12=>13
 g : 12*12=>13
 h : 12=>12
maximal types: {12,13}
Persistent Decomposition failed: Can't judge

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

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


Final result: Can't judge
/local-scratch/hzankl/2012/cops2012/107.trs: Failure(unknown)
(1 msec.)