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

TRS termination of:
[1] active(f(0)) -> mark(cons(0,f(s(0))))
[2] active(f(s(0))) -> mark(f(p(s(0))))
[3] active(p(s(0))) -> mark(0)
[4] mark(f(X)) -> active(f(mark(X)))
[5] mark(0) -> active(0)
[6] mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
[7] mark(s(X)) -> active(s(mark(X)))
[8] mark(p(X)) -> active(p(mark(X)))
[9] f(mark(X)) -> f(X)
[10] f(active(X)) -> f(X)
[11] cons(mark(X1),X2) -> cons(X1,X2)
[12] cons(X1,mark(X2)) -> cons(X1,X2)
[13] cons(active(X1),X2) -> cons(X1,X2)
[14] cons(X1,active(X2)) -> cons(X1,X2)
[15] s(mark(X)) -> s(X)
[16] s(active(X)) -> s(X)
[17] p(mark(X)) -> p(X)
[18] p(active(X)) -> p(X)


Sub problem: 
guided: 

DP termination of:
<Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(0)) , Marked_cons(0,f(s(0)))>
<Marked_active(f(0)) , Marked_f(s(0))>
<Marked_active(f(0)) , Marked_s(0)>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_active(f(s(0))) , Marked_f(p(s(0)))>
<Marked_active(f(s(0))) , Marked_p(s(0))>
<Marked_active(p(s(0))) , Marked_mark(0)>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(0) , Marked_active(0)>
<Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
<Marked_mark(cons(X1,X2)) , Marked_cons(mark(X1),X2)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_s(mark(X))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_p(mark(X))>
<Marked_mark(p(X)) , Marked_mark(X)>
<Marked_f(mark(X)) , Marked_f(X)>
<Marked_f(active(X)) , Marked_f(X)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)>
<Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
<Marked_p(mark(X)) , Marked_p(X)>
<Marked_p(active(X)) , Marked_p(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 5 components:

{  <Marked_mark(p(X)) , Marked_mark(X)> 
      --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
}

{  <Marked_f(active(X)) , Marked_f(X)> --> <Marked_f(active(X)) , Marked_f(X)>
  <Marked_f(active(X)) , Marked_f(X)> --> <Marked_f(mark(X)) , Marked_f(X)>
  <Marked_f(mark(X)) , Marked_f(X)> --> <Marked_f(active(X)) , Marked_f(X)>
  <Marked_f(mark(X)) , Marked_f(X)> --> <Marked_f(mark(X)) , Marked_f(X)>
}

{  <Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)> 
      --> <Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)>
  <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)> 
     --> <Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
}

{  <Marked_s(active(X)) , Marked_s(X)> --> <Marked_s(active(X)) , Marked_s(X)>
  <Marked_s(active(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(active(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
}

{  <Marked_p(active(X)) , Marked_p(X)> --> <Marked_p(active(X)) , Marked_p(X)>
  <Marked_p(active(X)) , Marked_p(X)> --> <Marked_p(mark(X)) , Marked_p(X)>
  <Marked_p(mark(X)) , Marked_p(X)> --> <Marked_p(active(X)) , Marked_p(X)>
  <Marked_p(mark(X)) , Marked_p(X)> --> <Marked_p(mark(X)) , Marked_p(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ;
  mark(0) >= active(0) ;
  mark(f(X)) >= active(f(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  cons(mark(X1),X2) >= cons(X1,X2) ;
  cons(active(X1),X2) >= cons(X1,X2) ;
  cons(X1,mark(X2)) >= cons(X1,X2) ;
  cons(X1,active(X2)) >= cons(X1,X2) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  active(f(0)) >= mark(cons(0,f(s(0)))) ;
  active(f(s(0))) >= mark(f(p(s(0)))) ;
  active(p(s(0))) >= mark(0) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
  Marked_mark(f(X)) >= Marked_active(f(mark(X))) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(s(X)) >= Marked_active(s(mark(X))) ;
  Marked_mark(p(X)) >= Marked_mark(X) ;
  Marked_mark(p(X)) >= Marked_active(p(mark(X))) ;
  Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0)))) ;
  Marked_active(f(s(0))) >= Marked_mark(f(p(s(0)))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(cons(X1,X2)) > Marked_active(cons(mark(X1),X2)) ;
 }
{
  Marked_mark(f(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(f(X)) > Marked_active(f(mark(X))) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(s(X)) > Marked_active(s(mark(X))) ;
 }
{
  Marked_mark(p(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(p(X)) > Marked_active(p(mark(X))) ;
 }
{
  Marked_active(f(0)) > Marked_mark(cons(0,f(s(0)))) ;
 }
{
  Marked_active(f(s(0))) > Marked_mark(f(p(s(0)))) ;
 }
 } 
=== 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(cons(X1,X2)) >= active(cons(mark(X1),X2))
constraint: mark(0) >= active(0)
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(p(X)) >= active(p(mark(X)))
constraint: cons(mark(X1),X2) >= cons(X1,X2)
constraint: cons(active(X1),X2) >= cons(X1,X2)
constraint: cons(X1,mark(X2)) >= cons(X1,X2)
constraint: cons(X1,active(X2)) >= cons(X1,X2)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: active(f(0)) >= mark(cons(0,f(s(0))))
constraint: active(f(s(0))) >= mark(f(p(s(0))))
constraint: active(p(s(0))) >= mark(0)
constraint: p(mark(X)) >= p(X)
constraint: p(active(X)) >= p(X)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2))
constraint: Marked_mark(f(X)) >= Marked_mark(X)
constraint: Marked_mark(f(X)) >= Marked_active(f(mark(X)))
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(s(X)) >= Marked_active(s(mark(X)))
constraint: Marked_mark(p(X)) >= Marked_mark(X)
constraint: Marked_mark(p(X)) >= Marked_active(p(mark(X)))
constraint: Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0))))
constraint: Marked_active(f(s(0))) >= Marked_mark(f(p(s(0))))
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_cons -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_s -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_p -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(p(X)) , Marked_mark(X)> 
      --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ;
  mark(0) >= active(0) ;
  mark(f(X)) >= active(f(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  cons(mark(X1),X2) >= cons(X1,X2) ;
  cons(active(X1),X2) >= cons(X1,X2) ;
  cons(X1,mark(X2)) >= cons(X1,X2) ;
  cons(X1,active(X2)) >= cons(X1,X2) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  active(f(0)) >= mark(cons(0,f(s(0)))) ;
  active(f(s(0))) >= mark(f(p(s(0)))) ;
  active(p(s(0))) >= mark(0) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
  Marked_mark(f(X)) >= Marked_active(f(mark(X))) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(p(X)) >= Marked_mark(X) ;
  Marked_mark(p(X)) >= Marked_active(p(mark(X))) ;
  Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0)))) ;
  Marked_active(f(s(0))) >= Marked_mark(f(p(s(0)))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(cons(X1,X2)) > Marked_active(cons(mark(X1),X2)) ;
 }
{
  Marked_mark(f(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(f(X)) > Marked_active(f(mark(X))) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(p(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(p(X)) > Marked_active(p(mark(X))) ;
 }
{
  Marked_active(f(0)) > Marked_mark(cons(0,f(s(0)))) ;
 }
{
  Marked_active(f(s(0))) > Marked_mark(f(p(s(0)))) ;
 }
 } 
=== 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(cons(X1,X2)) >= active(cons(mark(X1),X2))
constraint: mark(0) >= active(0)
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(p(X)) >= active(p(mark(X)))
constraint: cons(mark(X1),X2) >= cons(X1,X2)
constraint: cons(active(X1),X2) >= cons(X1,X2)
constraint: cons(X1,mark(X2)) >= cons(X1,X2)
constraint: cons(X1,active(X2)) >= cons(X1,X2)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: active(f(0)) >= mark(cons(0,f(s(0))))
constraint: active(f(s(0))) >= mark(f(p(s(0))))
constraint: active(p(s(0))) >= mark(0)
constraint: p(mark(X)) >= p(X)
constraint: p(active(X)) >= p(X)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2))
constraint: Marked_mark(f(X)) >= Marked_mark(X)
constraint: Marked_mark(f(X)) >= Marked_active(f(mark(X)))
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(p(X)) >= Marked_mark(X)
constraint: Marked_mark(p(X)) >= Marked_active(p(mark(X)))
constraint: Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0))))
constraint: Marked_active(f(s(0))) >= Marked_mark(f(p(s(0))))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(p(X)) , Marked_mark(X)> 
      --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ;
  mark(0) >= active(0) ;
  mark(f(X)) >= active(f(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  cons(mark(X1),X2) >= cons(X1,X2) ;
  cons(active(X1),X2) >= cons(X1,X2) ;
  cons(X1,mark(X2)) >= cons(X1,X2) ;
  cons(X1,active(X2)) >= cons(X1,X2) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  active(f(0)) >= mark(cons(0,f(s(0)))) ;
  active(f(s(0))) >= mark(f(p(s(0)))) ;
  active(p(s(0))) >= mark(0) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2)) ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
  Marked_mark(f(X)) >= Marked_active(f(mark(X))) ;
  Marked_mark(p(X)) >= Marked_mark(X) ;
  Marked_mark(p(X)) >= Marked_active(p(mark(X))) ;
  Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0)))) ;
  Marked_active(f(s(0))) >= Marked_mark(f(p(s(0)))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(cons(X1,X2)) > Marked_active(cons(mark(X1),X2)) ;
 }
{
  Marked_mark(f(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(f(X)) > Marked_active(f(mark(X))) ;
 }
{
  Marked_mark(p(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(p(X)) > Marked_active(p(mark(X))) ;
 }
{
  Marked_active(f(0)) > Marked_mark(cons(0,f(s(0)))) ;
 }
{
  Marked_active(f(s(0))) > Marked_mark(f(p(s(0)))) ;
 }
 } 
=== 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(cons(X1,X2)) >= active(cons(mark(X1),X2))
constraint: mark(0) >= active(0)
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(p(X)) >= active(p(mark(X)))
constraint: cons(mark(X1),X2) >= cons(X1,X2)
constraint: cons(active(X1),X2) >= cons(X1,X2)
constraint: cons(X1,mark(X2)) >= cons(X1,X2)
constraint: cons(X1,active(X2)) >= cons(X1,X2)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: active(f(0)) >= mark(cons(0,f(s(0))))
constraint: active(f(s(0))) >= mark(f(p(s(0))))
constraint: active(p(s(0))) >= mark(0)
constraint: p(mark(X)) >= p(X)
constraint: p(active(X)) >= p(X)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(cons(X1,X2)) >= Marked_active(cons(mark(X1),X2))
constraint: Marked_mark(f(X)) >= Marked_mark(X)
constraint: Marked_mark(f(X)) >= Marked_active(f(mark(X)))
constraint: Marked_mark(p(X)) >= Marked_mark(X)
constraint: Marked_mark(p(X)) >= Marked_active(p(mark(X)))
constraint: Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0))))
constraint: Marked_active(f(s(0))) >= Marked_mark(f(p(s(0))))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(p(X)) , Marked_mark(X)> 
      --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(p(X)) , Marked_active(p(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_active(p(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ;
  mark(0) >= active(0) ;
  mark(f(X)) >= active(f(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  cons(mark(X1),X2) >= cons(X1,X2) ;
  cons(active(X1),X2) >= cons(X1,X2) ;
  cons(X1,mark(X2)) >= cons(X1,X2) ;
  cons(X1,active(X2)) >= cons(X1,X2) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  active(f(0)) >= mark(cons(0,f(s(0)))) ;
  active(f(s(0))) >= mark(f(p(s(0)))) ;
  active(p(s(0))) >= mark(0) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
  Marked_mark(f(X)) >= Marked_active(f(mark(X))) ;
  Marked_mark(p(X)) >= Marked_mark(X) ;
  Marked_mark(p(X)) >= Marked_active(p(mark(X))) ;
  Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0)))) ;
  Marked_active(f(s(0))) >= Marked_mark(f(p(s(0)))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(f(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(f(X)) > Marked_active(f(mark(X))) ;
 }
{
  Marked_mark(p(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(p(X)) > Marked_active(p(mark(X))) ;
 }
{
  Marked_active(f(0)) > Marked_mark(cons(0,f(s(0)))) ;
 }
{
  Marked_active(f(s(0))) > Marked_mark(f(p(s(0)))) ;
 }
 } 
=== 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(cons(X1,X2)) >= active(cons(mark(X1),X2))
constraint: mark(0) >= active(0)
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(p(X)) >= active(p(mark(X)))
constraint: cons(mark(X1),X2) >= cons(X1,X2)
constraint: cons(active(X1),X2) >= cons(X1,X2)
constraint: cons(X1,mark(X2)) >= cons(X1,X2)
constraint: cons(X1,active(X2)) >= cons(X1,X2)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: active(f(0)) >= mark(cons(0,f(s(0))))
constraint: active(f(s(0))) >= mark(f(p(s(0))))
constraint: active(p(s(0))) >= mark(0)
constraint: p(mark(X)) >= p(X)
constraint: p(active(X)) >= p(X)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(f(X)) >= Marked_mark(X)
constraint: Marked_mark(f(X)) >= Marked_active(f(mark(X)))
constraint: Marked_mark(p(X)) >= Marked_mark(X)
constraint: Marked_mark(p(X)) >= Marked_active(p(mark(X)))
constraint: Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0))))
constraint: Marked_active(f(s(0))) >= Marked_mark(f(p(s(0))))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(p(X)) , Marked_mark(X)> 
      --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ;
  mark(0) >= active(0) ;
  mark(f(X)) >= active(f(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  cons(mark(X1),X2) >= cons(X1,X2) ;
  cons(active(X1),X2) >= cons(X1,X2) ;
  cons(X1,mark(X2)) >= cons(X1,X2) ;
  cons(X1,active(X2)) >= cons(X1,X2) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  active(f(0)) >= mark(cons(0,f(s(0)))) ;
  active(f(s(0))) >= mark(f(p(s(0)))) ;
  active(p(s(0))) >= mark(0) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
  Marked_mark(f(X)) >= Marked_active(f(mark(X))) ;
  Marked_mark(p(X)) >= Marked_mark(X) ;
  Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0)))) ;
  Marked_active(f(s(0))) >= Marked_mark(f(p(s(0)))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(f(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(f(X)) > Marked_active(f(mark(X))) ;
 }
{
  Marked_mark(p(X)) > Marked_mark(X) ;
 }
{
  Marked_active(f(0)) > Marked_mark(cons(0,f(s(0)))) ;
 }
{
  Marked_active(f(s(0))) > Marked_mark(f(p(s(0)))) ;
 }
 } 
=== 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(cons(X1,X2)) >= active(cons(mark(X1),X2))
constraint: mark(0) >= active(0)
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(p(X)) >= active(p(mark(X)))
constraint: cons(mark(X1),X2) >= cons(X1,X2)
constraint: cons(active(X1),X2) >= cons(X1,X2)
constraint: cons(X1,mark(X2)) >= cons(X1,X2)
constraint: cons(X1,active(X2)) >= cons(X1,X2)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: active(f(0)) >= mark(cons(0,f(s(0))))
constraint: active(f(s(0))) >= mark(f(p(s(0))))
constraint: active(p(s(0))) >= mark(0)
constraint: p(mark(X)) >= p(X)
constraint: p(active(X)) >= p(X)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(f(X)) >= Marked_mark(X)
constraint: Marked_mark(f(X)) >= Marked_active(f(mark(X)))
constraint: Marked_mark(p(X)) >= Marked_mark(X)
constraint: Marked_active(f(0)) >= Marked_mark(cons(0,f(s(0))))
constraint: Marked_active(f(s(0))) >= Marked_mark(f(p(s(0))))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(p(X)) , Marked_mark(X)> 
      --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(f(X)) , Marked_mark(X)> --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_mark(f(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ;
  mark(0) >= active(0) ;
  mark(f(X)) >= active(f(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  cons(mark(X1),X2) >= cons(X1,X2) ;
  cons(active(X1),X2) >= cons(X1,X2) ;
  cons(X1,mark(X2)) >= cons(X1,X2) ;
  cons(X1,active(X2)) >= cons(X1,X2) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  active(f(0)) >= mark(cons(0,f(s(0)))) ;
  active(f(s(0))) >= mark(f(p(s(0)))) ;
  active(p(s(0))) >= mark(0) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(f(X)) >= Marked_mark(X) ;
  Marked_mark(f(X)) >= Marked_active(f(mark(X))) ;
  Marked_mark(p(X)) >= Marked_mark(X) ;
  Marked_active(f(s(0))) >= Marked_mark(f(p(s(0)))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(f(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(f(X)) > Marked_active(f(mark(X))) ;
 }
{
  Marked_mark(p(X)) > Marked_mark(X) ;
 }
{
  Marked_active(f(s(0))) > Marked_mark(f(p(s(0)))) ;
 }
 } 
=== 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(cons(X1,X2)) >= active(cons(mark(X1),X2))
constraint: mark(0) >= active(0)
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(p(X)) >= active(p(mark(X)))
constraint: cons(mark(X1),X2) >= cons(X1,X2)
constraint: cons(active(X1),X2) >= cons(X1,X2)
constraint: cons(X1,mark(X2)) >= cons(X1,X2)
constraint: cons(X1,active(X2)) >= cons(X1,X2)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: active(f(0)) >= mark(cons(0,f(s(0))))
constraint: active(f(s(0))) >= mark(f(p(s(0))))
constraint: active(p(s(0))) >= mark(0)
constraint: p(mark(X)) >= p(X)
constraint: p(active(X)) >= p(X)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(f(X)) >= Marked_mark(X)
constraint: Marked_mark(f(X)) >= Marked_active(f(mark(X)))
constraint: Marked_mark(p(X)) >= Marked_mark(X)
constraint: Marked_active(f(s(0))) >= Marked_mark(f(p(s(0))))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(p(X)) , Marked_mark(X)> 
      --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(p(X)) , Marked_mark(X)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(p(X)) , Marked_mark(X)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ;
  mark(0) >= active(0) ;
  mark(f(X)) >= active(f(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  cons(mark(X1),X2) >= cons(X1,X2) ;
  cons(active(X1),X2) >= cons(X1,X2) ;
  cons(X1,mark(X2)) >= cons(X1,X2) ;
  cons(X1,active(X2)) >= cons(X1,X2) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  active(f(0)) >= mark(cons(0,f(s(0)))) ;
  active(f(s(0))) >= mark(f(p(s(0)))) ;
  active(p(s(0))) >= mark(0) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(f(X)) >= Marked_active(f(mark(X))) ;
  Marked_mark(p(X)) >= Marked_mark(X) ;
  Marked_active(f(s(0))) >= Marked_mark(f(p(s(0)))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(f(X)) > Marked_active(f(mark(X))) ;
 }
{
  Marked_mark(p(X)) > Marked_mark(X) ;
 }
{
  Marked_active(f(s(0))) > Marked_mark(f(p(s(0)))) ;
 }
 } 
=== 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(cons(X1,X2)) >= active(cons(mark(X1),X2))
constraint: mark(0) >= active(0)
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(p(X)) >= active(p(mark(X)))
constraint: cons(mark(X1),X2) >= cons(X1,X2)
constraint: cons(active(X1),X2) >= cons(X1,X2)
constraint: cons(X1,mark(X2)) >= cons(X1,X2)
constraint: cons(X1,active(X2)) >= cons(X1,X2)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: active(f(0)) >= mark(cons(0,f(s(0))))
constraint: active(f(s(0))) >= mark(f(p(s(0))))
constraint: active(p(s(0))) >= mark(0)
constraint: p(mark(X)) >= p(X)
constraint: p(active(X)) >= p(X)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(f(X)) >= Marked_active(f(mark(X)))
constraint: Marked_mark(p(X)) >= Marked_mark(X)
constraint: Marked_active(f(s(0))) >= Marked_mark(f(p(s(0))))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
      --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
  <Marked_mark(f(X)) , Marked_active(f(mark(X)))> 
     --> <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))> 
     --> <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(cons(X1,X2)) >= active(cons(mark(X1),X2)) ;
  mark(0) >= active(0) ;
  mark(f(X)) >= active(f(mark(X))) ;
  mark(s(X)) >= active(s(mark(X))) ;
  mark(p(X)) >= active(p(mark(X))) ;
  cons(mark(X1),X2) >= cons(X1,X2) ;
  cons(active(X1),X2) >= cons(X1,X2) ;
  cons(X1,mark(X2)) >= cons(X1,X2) ;
  cons(X1,active(X2)) >= cons(X1,X2) ;
  f(mark(X)) >= f(X) ;
  f(active(X)) >= f(X) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  active(f(0)) >= mark(cons(0,f(s(0)))) ;
  active(f(s(0))) >= mark(f(p(s(0)))) ;
  active(p(s(0))) >= mark(0) ;
  p(mark(X)) >= p(X) ;
  p(active(X)) >= p(X) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(f(X)) >= Marked_active(f(mark(X))) ;
  Marked_active(f(s(0))) >= Marked_mark(f(p(s(0)))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(f(X)) > Marked_active(f(mark(X))) ;
 }
{
  Marked_active(f(s(0))) > Marked_mark(f(p(s(0)))) ;
 }
 } 
=== 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(cons(X1,X2)) >= active(cons(mark(X1),X2))
constraint: mark(0) >= active(0)
constraint: mark(f(X)) >= active(f(mark(X)))
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: mark(p(X)) >= active(p(mark(X)))
constraint: cons(mark(X1),X2) >= cons(X1,X2)
constraint: cons(active(X1),X2) >= cons(X1,X2)
constraint: cons(X1,mark(X2)) >= cons(X1,X2)
constraint: cons(X1,active(X2)) >= cons(X1,X2)
constraint: f(mark(X)) >= f(X)
constraint: f(active(X)) >= f(X)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: active(f(0)) >= mark(cons(0,f(s(0))))
constraint: active(f(s(0))) >= mark(f(p(s(0))))
constraint: active(p(s(0))) >= mark(0)
constraint: p(mark(X)) >= p(X)
constraint: p(active(X)) >= p(X)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(f(X)) >= Marked_active(f(mark(X)))
constraint: Marked_active(f(s(0))) >= Marked_mark(f(p(s(0))))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
      --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_mark -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

ST: Marked_cons -> 1

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(f(0)) -> mark(cons(0,f(s(0))))
[2] active(f(s(0))) -> mark(f(p(s(0))))
[3] active(p(s(0))) -> mark(0)
[4] mark(f(X)) -> active(f(mark(X)))
[5] mark(0) -> active(0)
[6] mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
[7] mark(s(X)) -> active(s(mark(X)))
[8] mark(p(X)) -> active(p(mark(X)))
[9] f(mark(X)) -> f(X)
[10] f(active(X)) -> f(X)
[11] cons(mark(X1),X2) -> cons(X1,X2)
[12] cons(X1,mark(X2)) -> cons(X1,X2)
[13] cons(active(X1),X2) -> cons(X1,X2)
[14] cons(X1,active(X2)) -> cons(X1,X2)
[15] s(mark(X)) -> s(X)
[16] s(active(X)) -> s(X)
[17] p(mark(X)) -> p(X)
[18] p(active(X)) -> p(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(0)) , Marked_cons(0,f(s(0)))>
<Marked_active(f(0)) , Marked_f(s(0))>
<Marked_active(f(0)) , Marked_s(0)>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_active(f(s(0))) , Marked_f(p(s(0)))>
<Marked_active(f(s(0))) , Marked_p(s(0))>
<Marked_active(p(s(0))) , Marked_mark(0)>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_f(mark(X))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(0) , Marked_active(0)>
<Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
<Marked_mark(cons(X1,X2)) , Marked_cons(mark(X1),X2)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_s(mark(X))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_p(mark(X))>
<Marked_mark(p(X)) , Marked_mark(X)>
<Marked_f(mark(X)) , Marked_f(X)>
<Marked_f(active(X)) , Marked_f(X)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)>
<Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
<Marked_p(mark(X)) , Marked_p(X)>
<Marked_p(active(X)) , Marked_p(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ Marked_active ] (X0) = 1*X0; 
 [ 0 ] () = 0; 
 [ p ] (X0) = 2; 
 [ cons ] (X0,X1) = 2; 
 [ active ] (X0) = 0; 
 [ f ] (X0) = 2; 
 [ Marked_mark ] (X0) = 2; 
 removing <Marked_mark(s(X)),Marked_active(s(mark(X)))>
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ s ] (X0) = 2*X0 + 2; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ p ] (X0) = 1*X0; 
 [ cons ] (X0,X1) = 2*X0; 
 [ active ] (X0) = 1*X0; 
 [ f ] (X0) = 1*X0; 
 [ Marked_mark ] (X0) = 2*X0; 
 removing <Marked_mark(s(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_active(cons(mark(X1),X2))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ Marked_active ] (X0) = 1*X0; 
 [ 0 ] () = 0; 
 [ p ] (X0) = 1; 
 [ cons ] (X0,X1) = 0; 
 [ active ] (X0) = 0; 
 [ f ] (X0) = 1; 
 [ Marked_mark ] (X0) = 1; 
 removing <Marked_mark(cons(X1,X2)),Marked_active(cons(mark(X1),X2))>
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_active(p(mark(X)))>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 0; 
 [ s ] (X0) = 0; 
 [ Marked_active ] (X0) = 2*X0; 
 [ 0 ] () = 0; 
 [ p ] (X0) = 0; 
 [ cons ] (X0,X1) = 0; 
 [ active ] (X0) = 0; 
 [ f ] (X0) = 1; 
 [ Marked_mark ] (X0) = 2; 
 removing <Marked_mark(p(X)),Marked_active(p(mark(X)))>
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(0)) , Marked_mark(cons(0,f(s(0))))>
<Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ s ] (X0) = 3*X0 + 2; 
 [ Marked_active ] (X0) = 1*X0; 
 [ 0 ] () = 2; 
 [ p ] (X0) = 1*X0; 
 [ cons ] (X0,X1) = 1*X0; 
 [ active ] (X0) = 1*X0; 
 [ f ] (X0) = 2*X0; 
 [ Marked_mark ] (X0) = 1*X0; 
 removing <Marked_active(f(0)),Marked_mark(cons(0,f(s(0))))>
 [ {
      
     DP termination of:
     <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(f(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ s ] (X0) = 0; 
 [ Marked_active ] (X0) = 2; 
 [ 0 ] () = 0; 
 [ p ] (X0) = 2*X0; 
 [ cons ] (X0,X1) = 2*X0; 
 [ active ] (X0) = 1*X0; 
 [ f ] (X0) = 2*X0 + 1; 
 [ Marked_mark ] (X0) = 2*X0; 
 removing <Marked_mark(f(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
<Marked_mark(p(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 2*X0; 
 [ s ] (X0) = 0; 
 [ Marked_active ] (X0) = 0; 
 [ 0 ] () = 0; 
 [ p ] (X0) = 1*X0 + 1; 
 [ cons ] (X0,X1) = 2*X1 + 1*X0; 
 [ active ] (X0) = 1*X0; 
 [ f ] (X0) = 0; 
 [ Marked_mark ] (X0) = 1*X0; 
 removing <Marked_mark(p(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(f(s(0))) , Marked_mark(f(p(s(0))))>
<Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 2*X0; 
 [ s ] (X0) = 1; 
 [ Marked_active ] (X0) = 1*X0; 
 [ 0 ] () = 0; 
 [ p ] (X0) = 0; 
 [ cons ] (X0,X1) = 2*X0; 
 [ active ] (X0) = 1*X0; 
 [ f ] (X0) = 2*X0; 
 [ Marked_mark ] (X0) = 2*X0; 
 removing <Marked_active(f(s(0))),Marked_mark(f(p(s(0))))>
 [ {
      
     DP termination of:
     <Marked_mark(f(X)) , Marked_active(f(mark(X)))>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_f(mark(X)) , Marked_f(X)>
<Marked_f(active(X)) , Marked_f(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(X1,mark(X2)) , Marked_cons(X1,X2)>
<Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(X1,active(X2)) , Marked_cons(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_cons(active(X1),X2) , Marked_cons(X1,X2)>
<Marked_cons(mark(X1),X2) , Marked_cons(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_p(mark(X)) , Marked_p(X)>
<Marked_p(active(X)) , Marked_p(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 1.315118 seconds (real time)
Cime Exit Status: 0