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

TRS termination of:
[1] a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
[2] a____(X,nil) -> mark(X)
[3] a____(nil,X) -> mark(X)
[4] a__and(tt,X) -> mark(X)
[5] a__isNePal(__(I,__(P,I))) -> tt
[6] mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
[7] mark(and(X1,X2)) -> a__and(mark(X1),X2)
[8] mark(isNePal(X)) -> a__isNePal(mark(X))
[9] mark(nil) -> nil
[10] mark(tt) -> tt
[11] a____(X1,X2) -> __(X1,X2)
[12] a__and(X1,X2) -> and(X1,X2)
[13] a__isNePal(X) -> isNePal(X)


Sub problem: 
guided: 

DP termination of:
<Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))>
<Marked_a____(__(X,Y),Z) , Marked_mark(X)>
<Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))>
<Marked_a____(__(X,Y),Z) , Marked_mark(Y)>
<Marked_a____(__(X,Y),Z) , Marked_mark(Z)>
<Marked_a____(X,nil) , Marked_mark(X)>
<Marked_a____(nil,X) , Marked_mark(X)>
<Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
<Marked_mark(__(X1,X2)) , Marked_mark(X1)>
<Marked_mark(__(X1,X2)) , Marked_mark(X2)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNePal(X)) , Marked_a__isNePal(mark(X))>
<Marked_mark(isNePal(X)) , Marked_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(isNePal(X)) , Marked_mark(X)> 
      --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_mark(isNePal(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(isNePal(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(isNePal(X)) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(isNePal(X)) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(isNePal(X)) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_mark(__(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(__(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))> 
     --> <Marked_a____(nil,X) , Marked_mark(X)>
  <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))> 
     --> <Marked_a____(X,nil) , Marked_mark(X)>
  <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_mark(Z)>
  <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_mark(Y)>
  <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))>
  <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_mark(X)>
  <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),
                                     a____(mark(Y),mark(Z)))>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_a____(nil,X) , Marked_mark(X)> 
     --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_a____(nil,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(nil,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a____(nil,X) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_a____(nil,X) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(nil,X) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_a____(X,nil) , Marked_mark(X)> 
     --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_a____(X,nil) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(X,nil) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a____(X,nil) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_a____(X,nil) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(X,nil) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Z)> 
     --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Z)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Z)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Z)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Z)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Z)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Y)> 
     --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Y)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Y)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Y)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Y)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(Y)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))> 
     --> <Marked_a____(nil,X) , Marked_mark(X)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))> 
     --> <Marked_a____(X,nil) , Marked_mark(X)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_mark(Z)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_mark(Y)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_mark(X)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),
                                     a____(mark(Y),mark(Z)))>
  <Marked_a____(__(X,Y),Z) , Marked_mark(X)> 
     --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X2)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_mark(X1)>
  <Marked_a____(__(X,Y),Z) , Marked_mark(X)> 
     --> <Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))> 
     --> <Marked_a____(nil,X) , Marked_mark(X)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))> 
     --> <Marked_a____(X,nil) , Marked_mark(X)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_mark(Z)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_mark(Y)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_mark(X)>
  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))> 
     --> <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),
                                     a____(mark(Y),mark(Z)))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a____(__(X,Y),Z) >= a____(mark(X),a____(mark(Y),mark(Z))) ;
  a____(nil,X) >= mark(X) ;
  a____(X,nil) >= mark(X) ;
  a____(X1,X2) >= __(X1,X2) ;
  mark(__(X1,X2)) >= a____(mark(X1),mark(X2)) ;
  mark(nil) >= nil ;
  mark(tt) >= tt ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  mark(isNePal(X)) >= a__isNePal(mark(X)) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNePal(__(I,__(P,I))) >= tt ;
  a__isNePal(X) >= isNePal(X) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_a____(__(X,Y),Z) >= Marked_a____(mark(X),a____(mark(Y),mark(Z))) ;
  Marked_a____(__(X,Y),Z) >= Marked_a____(mark(Y),mark(Z)) ;
  Marked_a____(__(X,Y),Z) >= Marked_mark(X) ;
  Marked_a____(__(X,Y),Z) >= Marked_mark(Y) ;
  Marked_a____(__(X,Y),Z) >= Marked_mark(Z) ;
  Marked_a____(nil,X) >= Marked_mark(X) ;
  Marked_a____(X,nil) >= Marked_mark(X) ;
  Marked_mark(__(X1,X2)) >= Marked_a____(mark(X1),mark(X2)) ;
  Marked_mark(__(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(__(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(isNePal(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_a____(__(X,Y),Z) > Marked_a____(mark(X),a____(mark(Y),mark(Z))) ;
 }
{
  Marked_a____(__(X,Y),Z) > Marked_a____(mark(Y),mark(Z)) ;
 }
{
  Marked_a____(__(X,Y),Z) > Marked_mark(X) ;
 }
{
  Marked_a____(__(X,Y),Z) > Marked_mark(Y) ;
 }
{
  Marked_a____(__(X,Y),Z) > Marked_mark(Z) ;
 }
{
  Marked_a____(nil,X) > Marked_mark(X) ;
 }
{
  Marked_a____(X,nil) > Marked_mark(X) ;
 }
{
  Marked_mark(__(X1,X2)) > Marked_a____(mark(X1),mark(X2)) ;
 }
{
  Marked_mark(__(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(__(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(isNePal(X)) > Marked_mark(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: a____(__(X,Y),Z) >= a____(mark(X),a____(mark(Y),mark(Z)))
constraint: a____(nil,X) >= mark(X)
constraint: a____(X,nil) >= mark(X)
constraint: a____(X1,X2) >= __(X1,X2)
constraint: mark(__(X1,X2)) >= a____(mark(X1),mark(X2))
constraint: mark(nil) >= nil
constraint: mark(tt) >= tt
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: mark(isNePal(X)) >= a__isNePal(mark(X))
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNePal(__(I,__(P,I))) >= tt
constraint: a__isNePal(X) >= isNePal(X)
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_a____(__(X,Y),Z) >= Marked_a____(mark(X),
                                        a____(mark(Y),mark(Z)))
constraint: Marked_a____(__(X,Y),Z) >= Marked_a____(mark(Y),mark(Z))
constraint: Marked_a____(__(X,Y),Z) >= Marked_mark(X)
constraint: Marked_a____(__(X,Y),Z) >= Marked_mark(Y)
constraint: Marked_a____(__(X,Y),Z) >= Marked_mark(Z)
constraint: Marked_a____(nil,X) >= Marked_mark(X)
constraint: Marked_a____(X,nil) >= Marked_mark(X)
constraint: Marked_mark(__(X1,X2)) >= Marked_a____(mark(X1),mark(X2))
constraint: Marked_mark(__(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(__(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(isNePal(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))> 
      --> <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),
                                      a____(mark(Y),mark(Z)))>
}

{  <Marked_mark(isNePal(X)) , Marked_mark(X)> 
      --> <Marked_mark(isNePal(X)) , Marked_mark(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a____(__(X,Y),Z) >= a____(mark(X),a____(mark(Y),mark(Z))) ;
  a____(nil,X) >= mark(X) ;
  a____(X,nil) >= mark(X) ;
  a____(X1,X2) >= __(X1,X2) ;
  mark(__(X1,X2)) >= a____(mark(X1),mark(X2)) ;
  mark(nil) >= nil ;
  mark(tt) >= tt ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  mark(isNePal(X)) >= a__isNePal(mark(X)) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNePal(__(I,__(P,I))) >= tt ;
  a__isNePal(X) >= isNePal(X) ;
  Marked_a____(__(X,Y),Z) >= Marked_a____(mark(X),a____(mark(Y),mark(Z))) ;
 }
 + Disjunctions:{ 
{
  Marked_a____(__(X,Y),Z) > Marked_a____(mark(X),a____(mark(Y),mark(Z))) ;
 }
 } 
=== 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: a____(__(X,Y),Z) >= a____(mark(X),a____(mark(Y),mark(Z)))
constraint: a____(nil,X) >= mark(X)
constraint: a____(X,nil) >= mark(X)
constraint: a____(X1,X2) >= __(X1,X2)
constraint: mark(__(X1,X2)) >= a____(mark(X1),mark(X2))
constraint: mark(nil) >= nil
constraint: mark(tt) >= tt
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: mark(isNePal(X)) >= a__isNePal(mark(X))
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNePal(__(I,__(P,I))) >= tt
constraint: a__isNePal(X) >= isNePal(X)
constraint: Marked_a____(__(X,Y),Z) >= Marked_a____(mark(X),
                                        a____(mark(Y),mark(Z)))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a____(__(X,Y),Z) >= a____(mark(X),a____(mark(Y),mark(Z))) ;
  a____(nil,X) >= mark(X) ;
  a____(X,nil) >= mark(X) ;
  a____(X1,X2) >= __(X1,X2) ;
  mark(__(X1,X2)) >= a____(mark(X1),mark(X2)) ;
  mark(nil) >= nil ;
  mark(tt) >= tt ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  mark(isNePal(X)) >= a__isNePal(mark(X)) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__isNePal(__(I,__(P,I))) >= tt ;
  a__isNePal(X) >= isNePal(X) ;
  Marked_mark(isNePal(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(isNePal(X)) > Marked_mark(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: a____(__(X,Y),Z) >= a____(mark(X),a____(mark(Y),mark(Z)))
constraint: a____(nil,X) >= mark(X)
constraint: a____(X,nil) >= mark(X)
constraint: a____(X1,X2) >= __(X1,X2)
constraint: mark(__(X1,X2)) >= a____(mark(X1),mark(X2))
constraint: mark(nil) >= nil
constraint: mark(tt) >= tt
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: mark(isNePal(X)) >= a__isNePal(mark(X))
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__isNePal(__(I,__(P,I))) >= tt
constraint: a__isNePal(X) >= isNePal(X)
constraint: Marked_mark(isNePal(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
[2] a____(X,nil) -> mark(X)
[3] a____(nil,X) -> mark(X)
[4] a__and(tt,X) -> mark(X)
[5] a__isNePal(__(I,__(P,I))) -> tt
[6] mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
[7] mark(and(X1,X2)) -> a__and(mark(X1),X2)
[8] mark(isNePal(X)) -> a__isNePal(mark(X))
[9] mark(nil) -> nil
[10] mark(tt) -> tt
[11] a____(X1,X2) -> __(X1,X2)
[12] a__and(X1,X2) -> and(X1,X2)
[13] a__isNePal(X) -> isNePal(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))>
<Marked_a____(__(X,Y),Z) , Marked_mark(X)>
<Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))>
<Marked_a____(__(X,Y),Z) , Marked_mark(Y)>
<Marked_a____(__(X,Y),Z) , Marked_mark(Z)>
<Marked_a____(X,nil) , Marked_mark(X)>
<Marked_a____(nil,X) , Marked_mark(X)>
<Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
<Marked_mark(__(X1,X2)) , Marked_mark(X1)>
<Marked_mark(__(X1,X2)) , Marked_mark(X2)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNePal(X)) , Marked_a__isNePal(mark(X))>
<Marked_mark(isNePal(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))>
<Marked_a____(__(X,Y),Z) , Marked_mark(X)>
<Marked_a____(__(X,Y),Z) , Marked_a____(mark(Y),mark(Z))>
<Marked_a____(__(X,Y),Z) , Marked_mark(Y)>
<Marked_a____(__(X,Y),Z) , Marked_mark(Z)>
<Marked_a____(X,nil) , Marked_mark(X)>
<Marked_a____(nil,X) , Marked_mark(X)>
<Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_mark(__(X1,X2)) , Marked_a____(mark(X1),mark(X2))>
<Marked_mark(__(X1,X2)) , Marked_mark(X1)>
<Marked_mark(__(X1,X2)) , Marked_mark(X2)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(isNePal(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ a____ ] (X0,X1) = 1*X1 + 1*X0 + 3; 
 [ isNePal ] (X0) = 3*X0; 
 [ a__and ] (X0,X1) = 3*X1 + 2*X0 + 2; 
 [ Marked_mark ] (X0) = 2*X0; 
 [ __ ] (X0,X1) = 1*X1 + 1*X0 + 3; 
 [ Marked_a__and ] (X0,X1) = 3*X1 + 2*X0 + 3; 
 [ a__isNePal ] (X0) = 3*X0; 
 [ mark ] (X0) = 1*X0; 
 [ tt ] () = 0; 
 [ nil ] () = 1; 
 [ Marked_a____ ] (X0,X1) = 2*X1 + 2*X0; 
 [ and ] (X0,X1) = 3*X1 + 2*X0 + 2; 
 removing <Marked_a____(__(X,Y),Z),Marked_mark(X)><Marked_a____(__(X,Y),Z),
Marked_a____(mark(Y),mark(Z))><Marked_a____(__(X,Y),Z),Marked_mark(Y)><
Marked_a____(__(X,Y),Z),Marked_mark(Z)><Marked_a____(X,nil),Marked_mark(X)><
Marked_a____(nil,X),Marked_mark(X)><Marked_a__and(tt,X),Marked_mark(X)><
Marked_mark(__(X1,X2)),Marked_a____(mark(X1),mark(X2))><Marked_mark(__(X1,X2)),
Marked_mark(X1)><Marked_mark(__(X1,X2)),Marked_mark(X2)><Marked_mark(
                                                          and(X1,X2)),
Marked_a__and(mark(X1),X2)><Marked_mark(and(X1,X2)),Marked_mark(X1)>
 [ {
      
     DP termination of:
     <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))>
<Marked_mark(isNePal(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a____(__(X,Y),Z) , Marked_a____(mark(X),a____(mark(Y),mark(Z)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ a____ ] (X0,X1) = 1 + 2*X0 + 1*X1 + 0; 
 [ isNePal ] (X0) = 0; 
 [ a__and ] (X0,X1) = 3*X1 + 0; 
 [ __ ] (X0,X1) = 1 + 2*X0 + 1*X1 + 0; 
 [ a__isNePal ] (X0) = 0; 
 [ mark ] (X0) = 1*X0 + 0; 
 [ tt ] () = 0; 
 [ nil ] () = 0; 
 [ Marked_a____ ] (X0,X1) = 1*X0 + 0; 
 [ and ] (X0,X1) = 3*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_mark(isNePal(X)) , Marked_mark(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ a____ ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ isNePal ] (X0) = 2 + 2*X0 + 0; 
 [ a__and ] (X0,X1) = 3*X1 + 0; 
 [ Marked_mark ] (X0) = 3*X0 + 0; 
 [ __ ] (X0,X1) = 1*X0 + 1*X1 + 0; 
 [ a__isNePal ] (X0) = 2 + 2*X0 + 0; 
 [ mark ] (X0) = 1*X0 + 0; 
 [ tt ] () = 0; 
 [ nil ] () = 0; 
 [ and ] (X0,X1) = 3*X1 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.181304 seconds (real time)
Cime Exit Status: 0