- : unit = ()
- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
[2] active(__(X,nil)) -> mark(X)
[3] active(__(nil,X)) -> mark(X)
[4] active(U11(tt)) -> mark(U12(tt))
[5] active(U12(tt)) -> mark(tt)
[6] active(isNePal(__(I,__(P,I)))) -> mark(U11(tt))
[7] active(__(X1,X2)) -> __(active(X1),X2)
[8] active(__(X1,X2)) -> __(X1,active(X2))
[9] active(U11(X)) -> U11(active(X))
[10] active(U12(X)) -> U12(active(X))
[11] active(isNePal(X)) -> isNePal(active(X))
[12] __(mark(X1),X2) -> mark(__(X1,X2))
[13] __(X1,mark(X2)) -> mark(__(X1,X2))
[14] U11(mark(X)) -> mark(U11(X))
[15] U12(mark(X)) -> mark(U12(X))
[16] isNePal(mark(X)) -> mark(isNePal(X))
[17] proper(__(X1,X2)) -> __(proper(X1),proper(X2))
[18] proper(nil) -> ok(nil)
[19] proper(U11(X)) -> U11(proper(X))
[20] proper(tt) -> ok(tt)
[21] proper(U12(X)) -> U12(proper(X))
[22] proper(isNePal(X)) -> isNePal(proper(X))
[23] __(ok(X1),ok(X2)) -> ok(__(X1,X2))
[24] U11(ok(X)) -> ok(U11(X))
[25] U12(ok(X)) -> ok(U12(X))
[26] isNePal(ok(X)) -> ok(isNePal(X))
[27] top(mark(X)) -> top(proper(X))
[28] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(__(__(X,Y),Z)) , Marked___(X,__(Y,Z))>
<Marked_active(__(__(X,Y),Z)) , Marked___(Y,Z)>
<Marked_active(U11(tt)) , Marked_U12(tt)>
<Marked_active(isNePal(__(I,__(P,I)))) , Marked_U11(tt)>
<Marked_active(__(X1,X2)) , Marked___(active(X1),X2)>
<Marked_active(__(X1,X2)) , Marked_active(X1)>
<Marked_active(__(X1,X2)) , Marked___(X1,active(X2))>
<Marked_active(__(X1,X2)) , Marked_active(X2)>
<Marked_active(U11(X)) , Marked_U11(active(X))>
<Marked_active(U11(X)) , Marked_active(X)>
<Marked_active(U12(X)) , Marked_U12(active(X))>
<Marked_active(U12(X)) , Marked_active(X)>
<Marked_active(isNePal(X)) , Marked_isNePal(active(X))>
<Marked_active(isNePal(X)) , Marked_active(X)>
<Marked___(mark(X1),X2) , Marked___(X1,X2)>
<Marked___(X1,mark(X2)) , Marked___(X1,X2)>
<Marked_U11(mark(X)) , Marked_U11(X)>
<Marked_U12(mark(X)) , Marked_U12(X)>
<Marked_isNePal(mark(X)) , Marked_isNePal(X)>
<Marked_proper(__(X1,X2)) , Marked___(proper(X1),proper(X2))>
<Marked_proper(__(X1,X2)) , Marked_proper(X1)>
<Marked_proper(__(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U11(X)) , Marked_U11(proper(X))>
<Marked_proper(U11(X)) , Marked_proper(X)>
<Marked_proper(U12(X)) , Marked_U12(proper(X))>
<Marked_proper(U12(X)) , Marked_proper(X)>
<Marked_proper(isNePal(X)) , Marked_isNePal(proper(X))>
<Marked_proper(isNePal(X)) , Marked_proper(X)>
<Marked___(ok(X1),ok(X2)) , Marked___(X1,X2)>
<Marked_U11(ok(X)) , Marked_U11(X)>
<Marked_U12(ok(X)) , Marked_U12(X)>
<Marked_isNePal(ok(X)) , Marked_isNePal(X)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 7 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(ok(X)) , Marked_top(active(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
}

{  <Marked_proper(isNePal(X)) , Marked_proper(X)> 
      --> <Marked_proper(isNePal(X)) , Marked_proper(X)>
  <Marked_proper(isNePal(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(isNePal(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(isNePal(X)) , Marked_proper(X)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(isNePal(X)) , Marked_proper(X)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNePal(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U12(X)) , Marked_proper(X)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(isNePal(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(U11(X)) , Marked_proper(X)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(isNePal(X)) , Marked_proper(X)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(isNePal(X)) , Marked_proper(X)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U12(X)) , Marked_proper(X)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(U11(X)) , Marked_proper(X)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(__(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(__(X1,X2)) , Marked_proper(X1)>
}

{  <Marked_active(isNePal(X)) , Marked_active(X)> 
      --> <Marked_active(isNePal(X)) , Marked_active(X)>
  <Marked_active(isNePal(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(isNePal(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(isNePal(X)) , Marked_active(X)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X2)>
  <Marked_active(isNePal(X)) , Marked_active(X)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X1)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(isNePal(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X2)>
  <Marked_active(U12(X)) , Marked_active(X)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X1)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(isNePal(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X2)>
  <Marked_active(U11(X)) , Marked_active(X)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X1)>
  <Marked_active(__(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(isNePal(X)) , Marked_active(X)>
  <Marked_active(__(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(__(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(__(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X2)>
  <Marked_active(__(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X1)>
  <Marked_active(__(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(isNePal(X)) , Marked_active(X)>
  <Marked_active(__(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U12(X)) , Marked_active(X)>
  <Marked_active(__(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(U11(X)) , Marked_active(X)>
  <Marked_active(__(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X2)>
  <Marked_active(__(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(__(X1,X2)) , Marked_active(X1)>
}

{  <Marked___(ok(X1),ok(X2)) , Marked___(X1,X2)> 
      --> <Marked___(ok(X1),ok(X2)) , Marked___(X1,X2)>
  <Marked___(ok(X1),ok(X2)) , Marked___(X1,X2)> 
     --> <Marked___(X1,mark(X2)) , Marked___(X1,X2)>
  <Marked___(ok(X1),ok(X2)) , Marked___(X1,X2)> 
     --> <Marked___(mark(X1),X2) , Marked___(X1,X2)>
  <Marked___(X1,mark(X2)) , Marked___(X1,X2)> 
     --> <Marked___(ok(X1),ok(X2)) , Marked___(X1,X2)>
  <Marked___(X1,mark(X2)) , Marked___(X1,X2)> 
     --> <Marked___(X1,mark(X2)) , Marked___(X1,X2)>
  <Marked___(X1,mark(X2)) , Marked___(X1,X2)> 
     --> <Marked___(mark(X1),X2) , Marked___(X1,X2)>
  <Marked___(mark(X1),X2) , Marked___(X1,X2)> 
     --> <Marked___(ok(X1),ok(X2)) , Marked___(X1,X2)>
  <Marked___(mark(X1),X2) , Marked___(X1,X2)> 
     --> <Marked___(X1,mark(X2)) , Marked___(X1,X2)>
  <Marked___(mark(X1),X2) , Marked___(X1,X2)> 
     --> <Marked___(mark(X1),X2) , Marked___(X1,X2)>
}

{  <Marked_U11(ok(X)) , Marked_U11(X)> --> <Marked_U11(ok(X)) , Marked_U11(X)>
  <Marked_U11(ok(X)) , Marked_U11(X)> --> <Marked_U11(mark(X)) , Marked_U11(X)>
  <Marked_U11(mark(X)) , Marked_U11(X)> --> <Marked_U11(ok(X)) , Marked_U11(X)>
  <Marked_U11(mark(X)) , Marked_U11(X)> 
     --> <Marked_U11(mark(X)) , Marked_U11(X)>
}

{  <Marked_U12(ok(X)) , Marked_U12(X)> --> <Marked_U12(ok(X)) , Marked_U12(X)>
  <Marked_U12(ok(X)) , Marked_U12(X)> --> <Marked_U12(mark(X)) , Marked_U12(X)>
  <Marked_U12(mark(X)) , Marked_U12(X)> --> <Marked_U12(ok(X)) , Marked_U12(X)>
  <Marked_U12(mark(X)) , Marked_U12(X)> 
     --> <Marked_U12(mark(X)) , Marked_U12(X)>
}

{  <Marked_isNePal(ok(X)) , Marked_isNePal(X)> 
      --> <Marked_isNePal(ok(X)) , Marked_isNePal(X)>
  <Marked_isNePal(ok(X)) , Marked_isNePal(X)> 
     --> <Marked_isNePal(mark(X)) , Marked_isNePal(X)>
  <Marked_isNePal(mark(X)) , Marked_isNePal(X)> 
     --> <Marked_isNePal(ok(X)) , Marked_isNePal(X)>
  <Marked_isNePal(mark(X)) , Marked_isNePal(X)> 
     --> <Marked_isNePal(mark(X)) , Marked_isNePal(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  __(mark(X1),X2) >= mark(__(X1,X2)) ;
  __(ok(X1),ok(X2)) >= ok(__(X1,X2)) ;
  __(X1,mark(X2)) >= mark(__(X1,X2)) ;
  active(__(__(X,Y),Z)) >= mark(__(X,__(Y,Z))) ;
  active(__(nil,X)) >= mark(X) ;
  active(__(X,nil)) >= mark(X) ;
  active(__(X1,X2)) >= __(active(X1),X2) ;
  active(__(X1,X2)) >= __(X1,active(X2)) ;
  active(U12(tt)) >= mark(tt) ;
  active(U12(X)) >= U12(active(X)) ;
  active(U11(tt)) >= mark(U12(tt)) ;
  active(U11(X)) >= U11(active(X)) ;
  active(isNePal(__(I,__(P,I)))) >= mark(U11(tt)) ;
  active(isNePal(X)) >= isNePal(active(X)) ;
  U12(mark(X)) >= mark(U12(X)) ;
  U12(ok(X)) >= ok(U12(X)) ;
  U11(mark(X)) >= mark(U11(X)) ;
  U11(ok(X)) >= ok(U11(X)) ;
  isNePal(mark(X)) >= mark(isNePal(X)) ;
  isNePal(ok(X)) >= ok(isNePal(X)) ;
  proper(__(X1,X2)) >= __(proper(X1),proper(X2)) ;
  proper(nil) >= ok(nil) ;
  proper(U12(X)) >= U12(proper(X)) ;
  proper(tt) >= ok(tt) ;
  proper(U11(X)) >= U11(proper(X)) ;
  proper(isNePal(X)) >= isNePal(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: __(mark(X1),X2) >= mark(__(X1,X2))
constraint: __(ok(X1),ok(X2)) >= ok(__(X1,X2))
constraint: __(X1,mark(X2)) >= mark(__(X1,X2))
constraint: active(__(__(X,Y),Z)) >= mark(__(X,__(Y,Z)))
constraint: active(__(nil,X)) >= mark(X)
constraint: active(__(X,nil)) >= mark(X)
constraint: active(__(X1,X2)) >= __(active(X1),X2)
constraint: active(__(X1,X2)) >= __(X1,active(X2))
constraint: active(U12(tt)) >= mark(tt)
constraint: active(U12(X)) >= U12(active(X))
constraint: active(U11(tt)) >= mark(U12(tt))
constraint: active(U11(X)) >= U11(active(X))
constraint: active(isNePal(__(I,__(P,I)))) >= mark(U11(tt))
constraint: active(isNePal(X)) >= isNePal(active(X))
constraint: U12(mark(X)) >= mark(U12(X))
constraint: U12(ok(X)) >= ok(U12(X))
constraint: U11(mark(X)) >= mark(U11(X))
constraint: U11(ok(X)) >= ok(U11(X))
constraint: isNePal(mark(X)) >= mark(isNePal(X))
constraint: isNePal(ok(X)) >= ok(isNePal(X))
constraint: proper(__(X1,X2)) >= __(proper(X1),proper(X2))
constraint: proper(nil) >= ok(nil)
constraint: proper(U12(X)) >= U12(proper(X))
constraint: proper(tt) >= ok(tt)
constraint: proper(U11(X)) >= U11(proper(X))
constraint: proper(isNePal(X)) >= isNePal(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_top(mark(X)) >= Marked_top(proper(X))
constraint: Marked_top(ok(X)) >= Marked_top(active(X))
APPLY CRITERIA (Subterm criterion)

ST: Marked_proper -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_active -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked___ -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_U11 -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_U12 -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_isNePal -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  __(mark(X1),X2) >= mark(__(X1,X2)) ;
  __(ok(X1),ok(X2)) >= ok(__(X1,X2)) ;
  __(X1,mark(X2)) >= mark(__(X1,X2)) ;
  active(__(__(X,Y),Z)) >= mark(__(X,__(Y,Z))) ;
  active(__(nil,X)) >= mark(X) ;
  active(__(X,nil)) >= mark(X) ;
  active(__(X1,X2)) >= __(active(X1),X2) ;
  active(__(X1,X2)) >= __(X1,active(X2)) ;
  active(U12(tt)) >= mark(tt) ;
  active(U12(X)) >= U12(active(X)) ;
  active(U11(tt)) >= mark(U12(tt)) ;
  active(U11(X)) >= U11(active(X)) ;
  active(isNePal(__(I,__(P,I)))) >= mark(U11(tt)) ;
  active(isNePal(X)) >= isNePal(active(X)) ;
  U12(mark(X)) >= mark(U12(X)) ;
  U12(ok(X)) >= ok(U12(X)) ;
  U11(mark(X)) >= mark(U11(X)) ;
  U11(ok(X)) >= ok(U11(X)) ;
  isNePal(mark(X)) >= mark(isNePal(X)) ;
  isNePal(ok(X)) >= ok(isNePal(X)) ;
  proper(__(X1,X2)) >= __(proper(X1),proper(X2)) ;
  proper(nil) >= ok(nil) ;
  proper(U12(X)) >= U12(proper(X)) ;
  proper(tt) >= ok(tt) ;
  proper(U11(X)) >= U11(proper(X)) ;
  proper(isNePal(X)) >= isNePal(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(ok(X)) > Marked_top(active(X)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: __(mark(X1),X2) >= mark(__(X1,X2))
constraint: __(ok(X1),ok(X2)) >= ok(__(X1,X2))
constraint: __(X1,mark(X2)) >= mark(__(X1,X2))
constraint: active(__(__(X,Y),Z)) >= mark(__(X,__(Y,Z)))
constraint: active(__(nil,X)) >= mark(X)
constraint: active(__(X,nil)) >= mark(X)
constraint: active(__(X1,X2)) >= __(active(X1),X2)
constraint: active(__(X1,X2)) >= __(X1,active(X2))
constraint: active(U12(tt)) >= mark(tt)
constraint: active(U12(X)) >= U12(active(X))
constraint: active(U11(tt)) >= mark(U12(tt))
constraint: active(U11(X)) >= U11(active(X))
constraint: active(isNePal(__(I,__(P,I)))) >= mark(U11(tt))
constraint: active(isNePal(X)) >= isNePal(active(X))
constraint: U12(mark(X)) >= mark(U12(X))
constraint: U12(ok(X)) >= ok(U12(X))
constraint: U11(mark(X)) >= mark(U11(X))
constraint: U11(ok(X)) >= ok(U11(X))
constraint: isNePal(mark(X)) >= mark(isNePal(X))
constraint: isNePal(ok(X)) >= ok(isNePal(X))
constraint: proper(__(X1,X2)) >= __(proper(X1),proper(X2))
constraint: proper(nil) >= ok(nil)
constraint: proper(U12(X)) >= U12(proper(X))
constraint: proper(tt) >= ok(tt)
constraint: proper(U11(X)) >= U11(proper(X))
constraint: proper(isNePal(X)) >= isNePal(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_top(ok(X)) >= Marked_top(active(X))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked___(mark(X1),X2) , Marked___(X1,X2)> 
      --> <Marked___(mark(X1),X2) , Marked___(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked___ -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z)))
[2] active(__(X,nil)) -> mark(X)
[3] active(__(nil,X)) -> mark(X)
[4] active(U11(tt)) -> mark(U12(tt))
[5] active(U12(tt)) -> mark(tt)
[6] active(isNePal(__(I,__(P,I)))) -> mark(U11(tt))
[7] active(__(X1,X2)) -> __(active(X1),X2)
[8] active(__(X1,X2)) -> __(X1,active(X2))
[9] active(U11(X)) -> U11(active(X))
[10] active(U12(X)) -> U12(active(X))
[11] active(isNePal(X)) -> isNePal(active(X))
[12] __(mark(X1),X2) -> mark(__(X1,X2))
[13] __(X1,mark(X2)) -> mark(__(X1,X2))
[14] U11(mark(X)) -> mark(U11(X))
[15] U12(mark(X)) -> mark(U12(X))
[16] isNePal(mark(X)) -> mark(isNePal(X))
[17] proper(__(X1,X2)) -> __(proper(X1),proper(X2))
[18] proper(nil) -> ok(nil)
[19] proper(U11(X)) -> U11(proper(X))
[20] proper(tt) -> ok(tt)
[21] proper(U12(X)) -> U12(proper(X))
[22] proper(isNePal(X)) -> isNePal(proper(X))
[23] __(ok(X1),ok(X2)) -> ok(__(X1,X2))
[24] U11(ok(X)) -> ok(U11(X))
[25] U12(ok(X)) -> ok(U12(X))
[26] isNePal(ok(X)) -> ok(isNePal(X))
[27] top(mark(X)) -> top(proper(X))
[28] top(ok(X)) -> top(active(X))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(__(__(X,Y),Z)) , Marked___(X,__(Y,Z))>
<Marked_active(__(__(X,Y),Z)) , Marked___(Y,Z)>
<Marked_active(U11(tt)) , Marked_U12(tt)>
<Marked_active(isNePal(__(I,__(P,I)))) , Marked_U11(tt)>
<Marked_active(__(X1,X2)) , Marked___(active(X1),X2)>
<Marked_active(__(X1,X2)) , Marked_active(X1)>
<Marked_active(__(X1,X2)) , Marked___(X1,active(X2))>
<Marked_active(__(X1,X2)) , Marked_active(X2)>
<Marked_active(U11(X)) , Marked_U11(active(X))>
<Marked_active(U11(X)) , Marked_active(X)>
<Marked_active(U12(X)) , Marked_U12(active(X))>
<Marked_active(U12(X)) , Marked_active(X)>
<Marked_active(isNePal(X)) , Marked_isNePal(active(X))>
<Marked_active(isNePal(X)) , Marked_active(X)>
<Marked___(mark(X1),X2) , Marked___(X1,X2)>
<Marked___(X1,mark(X2)) , Marked___(X1,X2)>
<Marked_U11(mark(X)) , Marked_U11(X)>
<Marked_U12(mark(X)) , Marked_U12(X)>
<Marked_isNePal(mark(X)) , Marked_isNePal(X)>
<Marked_proper(__(X1,X2)) , Marked___(proper(X1),proper(X2))>
<Marked_proper(__(X1,X2)) , Marked_proper(X1)>
<Marked_proper(__(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U11(X)) , Marked_U11(proper(X))>
<Marked_proper(U11(X)) , Marked_proper(X)>
<Marked_proper(U12(X)) , Marked_U12(proper(X))>
<Marked_proper(U12(X)) , Marked_proper(X)>
<Marked_proper(isNePal(X)) , Marked_isNePal(proper(X))>
<Marked_proper(isNePal(X)) , Marked_proper(X)>
<Marked___(ok(X1),ok(X2)) , Marked___(X1,X2)>
<Marked_U11(ok(X)) , Marked_U11(X)>
<Marked_U12(ok(X)) , Marked_U12(X)>
<Marked_isNePal(ok(X)) , Marked_isNePal(X)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0 + 1; 
 [ proper ] (X0) = 1*X0; 
 [ U12 ] (X0) = 3*X0 + 1; 
 [ active ] (X0) = 1*X0; 
 [ top ] (X0) = 0; 
 [ U11 ] (X0) = 1*X0 + 2; 
 [ __ ] (X0,X1) = 1*X1 + 3*X0 + 1; 
 [ ok ] (X0) = 1*X0; 
 [ tt ] () = 0; 
 [ nil ] () = 0; 
 [ Marked_top ] (X0) = 1*X0; 
 [ isNePal ] (X0) = 2*X0; 
 removing <Marked_top(mark(X)),Marked_top(proper(X))>
 [ {
      
     DP termination of:
     <Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 0; 
 [ proper ] (X0) = 2 + 3*X0 + 0; 
 [ U12 ] (X0) = 2 + 2*X0 + 0; 
 [ active ] (X0) = 2*X0 + 0; 
 [ top ] (X0) = 0; 
 [ U11 ] (X0) = 1*X0 + 0; 
 [ __ ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; 
 [ ok ] (X0) = 2 + 2*X0 + 0; 
 [ tt ] () = 0; 
 [ nil ] () = 0; 
 [ Marked_top ] (X0) = 3*X0 + 0; 
 [ isNePal ] (X0) = 1*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_proper(__(X1,X2)) , Marked_proper(X1)>
<Marked_proper(__(X1,X2)) , Marked_proper(X2)>
<Marked_proper(U11(X)) , Marked_proper(X)>
<Marked_proper(U12(X)) , Marked_proper(X)>
<Marked_proper(isNePal(X)) , Marked_proper(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_active(__(X1,X2)) , Marked_active(X1)>
<Marked_active(__(X1,X2)) , Marked_active(X2)>
<Marked_active(U11(X)) , Marked_active(X)>
<Marked_active(U12(X)) , Marked_active(X)>
<Marked_active(isNePal(X)) , Marked_active(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked___(mark(X1),X2) , Marked___(X1,X2)>
<Marked___(X1,mark(X2)) , Marked___(X1,X2)>
<Marked___(ok(X1),ok(X2)) , Marked___(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked___(mark(X1),X2) , Marked___(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked___(mark(X1),X2) , Marked___(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_U11(mark(X)) , Marked_U11(X)>
<Marked_U11(ok(X)) , Marked_U11(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_U12(mark(X)) , Marked_U12(X)>
<Marked_U12(ok(X)) , Marked_U12(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_isNePal(mark(X)) , Marked_isNePal(X)>
<Marked_isNePal(ok(X)) , Marked_isNePal(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.241737 seconds (real time)
Cime Exit Status: 0