(ignored inputs)COMMENT from p.208 of \cite{Klop80}
Rewrite Rules:
   [ Ap(Ap(Ap(S,?x),?y),?z) -> Ap(Ap(?x,?z),Ap(?y,?z)),
     Ap(Ap(K,?x),?y) -> ?x,
     Ap(I,?x) -> ?x,
     Ap(Ap(Dh,?z),?z) -> ?z ]
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...
   [ Ap(Ap(Ap(S,?x),?y),?z) -> Ap(Ap(?x,?z),Ap(?y,?z)),
     Ap(Ap(K,?x),?y) -> ?x,
     Ap(I,?x) -> ?x,
     Ap(Ap(Dh,?z),?z) -> ?z ]
Sort Assignment:
 I : =>15
 K : =>15
 S : =>15
 Ap : 15*15=>15
 Dh : =>15
maximal types: {15}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ Ap(Ap(Ap(S,?x),?y),?z) -> Ap(Ap(?x,?z),Ap(?y,?z)),
     Ap(Ap(K,?x),?y) -> ?x,
     Ap(I,?x) -> ?x,
     Ap(Ap(Dh,?z),?z) -> ?z ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ Ap(Ap(Ap(S,?x),?y),?z) -> Ap(Ap(?x,?z),Ap(?y,?z)),
     Ap(Ap(K,?x),?y) -> ?x,
     Ap(I,?x) -> ?x,
     Ap(Ap(Dh,?z),?z) -> ?z ]
Commutative Decomposition failed (not left-linear): Can't judge
No further decomposition possible


Final result: Can't judge
/local-scratch/hzankl/2012/cops2012/54.trs: Failure(unknown)
(42 msec.)