Rewrite Rules:
   [ F(D(?x),?y) -> F(D(?x),G(G(?y))),
     F(?x,E(?y)) -> F(G(?x),E(?y)),
     G(?x) -> ?x,
     H(I(?x)) -> K(J(?x)),
     J(?x) -> K(J(?x)),
     I(?x) -> I(J(?x)),
     J(?x) -> J(K(J(?x))),
     S(?x,T(?x)) -> T(?x) ]
Apply Direct Methods...
Inner CPs:
   [ H(I(J(?x_5))) = K(J(?x_5)) ]
Outer CPs:
   [ F(D(?x),G(G(E(?y_1)))) = F(G(D(?x)),E(?y_1)),
     K(J(?x_4)) = J(K(J(?x_4))) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth&Bendix
not Left-Linear, Right-Linear
unknown Simple-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(D(?x),?y) -> F(D(?x),G(G(?y))),
     F(?x,E(?y)) -> F(G(?x),E(?y)),
     G(?x) -> ?x,
     H(I(?x)) -> K(J(?x)),
     J(?x) -> K(J(?x)),
     I(?x) -> I(J(?x)),
     J(?x) -> J(K(J(?x))),
     S(?x,T(?x)) -> T(?x) ]
Sort Assignment:
 D : 11=>38
 E : 13=>38
 F : 38*38=>39
 G : 38=>38
 H : 35=>34
 I : 34=>35
 J : 34=>34
 K : 34=>34
 S : 31*33=>33
 T : 31=>33
maximal types: {31,33}{34,35}{11,13,38,39}
{31,33}
(ps)Rewrite Rules:
   [ S(?x,T(?x)) -> T(?x) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth&Bendix
Direct Methods: CR
{34,35}
(ps)Rewrite Rules:
   [ H(I(?x)) -> K(J(?x)),
     J(?x) -> K(J(?x)),
     I(?x) -> I(J(?x)),
     J(?x) -> J(K(J(?x))) ]
Apply Direct Methods...
Inner CPs:
   [ H(I(J(?x_2))) = K(J(?x_2)) ]
Outer CPs:
   [ K(J(?x_1)) = J(K(J(?x_1))) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth&Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ K(J(?x)) = J(K(J(?x))),
     K(J(?x)) = H(I(J(?x))),
     J(K(J(?x))) = K(J(?x)),
     H(I(J(?x))) = K(J(?x)) ]
Okui (Simultaneous CPs)
Direct Methods: CR
{11,13,38,39}
(ps)Rewrite Rules:
   [ F(D(?x),?y) -> F(D(?x),G(G(?y))),
     F(?x,E(?y)) -> F(G(?x),E(?y)),
     G(?x) -> ?x ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ F(D(?x),G(G(E(?y_1)))) = F(G(D(?x)),E(?y_1)) ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
unknown Knuth&Bendix
Linear
Development Closed
Direct Methods: CR
Result by Persistent Decomposition: CR

Final result: CR
/local-scratch/hzankl/2012/cops2012/94.trs: Success(CR)
(53 msec.)