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

TRS termination of:
[1] p(0) -> 0
[2] p(s(X)) -> X
[3] leq(0,Y) -> true
[4] leq(s(X),0) -> false
[5] leq(s(X),s(Y)) -> leq(X,Y)
[6] if(true,X,Y) -> activate(X)
[7] if(false,X,Y) -> activate(Y)
[8] diff(X,Y) -> if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y)))
[9] 0 -> n__0
[10] s(X) -> n__s(X)
[11] diff(X1,X2) -> n__diff(X1,X2)
[12] p(X) -> n__p(X)
[13] activate(n__0) -> 0
[14] activate(n__s(X)) -> s(activate(X))
[15] activate(n__diff(X1,X2)) -> diff(activate(X1),activate(X2))
[16] activate(n__p(X)) -> p(activate(X))
[17] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_leq(s(X),s(Y)) , Marked_leq(X,Y)>
<Marked_if(true,X,Y) , Marked_activate(X)>
<Marked_if(false,X,Y) , Marked_activate(Y)>
<Marked_diff(X,Y) , Marked_if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y)))>
<Marked_diff(X,Y) , Marked_leq(X,Y)>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__s(X)) , Marked_s(activate(X))>
<Marked_activate(n__s(X)) , Marked_activate(X)>
<Marked_activate(n__diff(X1,X2)) , Marked_diff(activate(X1),activate(X2))>
<Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)>
<Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)>
<Marked_activate(n__p(X)) , Marked_p(activate(X))>
<Marked_activate(n__p(X)) , Marked_activate(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_activate(n__p(X)) , Marked_activate(X)> 
      --> <Marked_activate(n__p(X)) , Marked_activate(X)>
  <Marked_activate(n__p(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__p(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__p(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_diff(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__p(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__p(X)) , Marked_activate(X)>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_diff(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__p(X)) , Marked_activate(X)>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_diff(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_activate(n__diff(X1,X2)) , Marked_diff(activate(X1),activate(X2))> 
     --> <Marked_diff(X,Y) , Marked_if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y)))>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__p(X)) , Marked_activate(X)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_diff(activate(X1),
                                             activate(X2))>
  <Marked_activate(n__s(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_diff(X,Y) , Marked_if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y)))> 
     --> <Marked_if(false,X,Y) , Marked_activate(Y)>
  <Marked_diff(X,Y) , Marked_if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y)))> 
     --> <Marked_if(true,X,Y) , Marked_activate(X)>
  <Marked_if(false,X,Y) , Marked_activate(Y)> 
     --> <Marked_activate(n__p(X)) , Marked_activate(X)>
  <Marked_if(false,X,Y) , Marked_activate(Y)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)>
  <Marked_if(false,X,Y) , Marked_activate(Y)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)>
  <Marked_if(false,X,Y) , Marked_activate(Y)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_diff(activate(X1),
                                             activate(X2))>
  <Marked_if(false,X,Y) , Marked_activate(Y)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
  <Marked_if(true,X,Y) , Marked_activate(X)> 
     --> <Marked_activate(n__p(X)) , Marked_activate(X)>
  <Marked_if(true,X,Y) , Marked_activate(X)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X2)>
  <Marked_if(true,X,Y) , Marked_activate(X)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_activate(X1)>
  <Marked_if(true,X,Y) , Marked_activate(X)> 
     --> <Marked_activate(n__diff(X1,X2)) , Marked_diff(activate(X1),
                                             activate(X2))>
  <Marked_if(true,X,Y) , Marked_activate(X)> 
     --> <Marked_activate(n__s(X)) , Marked_activate(X)>
}

{  <Marked_leq(s(X),s(Y)) , Marked_leq(X,Y)> 
      --> <Marked_leq(s(X),s(Y)) , Marked_leq(X,Y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  0 >= n__0 ;
  p(0) >= 0 ;
  p(s(X)) >= X ;
  p(X) >= n__p(X) ;
  s(X) >= n__s(X) ;
  leq(0,Y) >= true ;
  leq(s(X),0) >= false ;
  leq(s(X),s(Y)) >= leq(X,Y) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(activate(X)) ;
  activate(n__diff(X1,X2)) >= diff(activate(X1),activate(X2)) ;
  activate(n__p(X)) >= p(activate(X)) ;
  activate(X) >= X ;
  if(true,X,Y) >= activate(X) ;
  if(false,X,Y) >= activate(Y) ;
  diff(X,Y) >= if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y))) ;
  diff(X1,X2) >= n__diff(X1,X2) ;
  Marked_activate(n__s(X)) >= Marked_activate(X) ;
  Marked_activate(n__diff(X1,X2)) >= Marked_activate(X1) ;
  Marked_activate(n__diff(X1,X2)) >= Marked_activate(X2) ;
  Marked_activate(n__diff(X1,X2)) >= Marked_diff(activate(X1),activate(X2)) ;
  Marked_activate(n__p(X)) >= Marked_activate(X) ;
  Marked_diff(X,Y) >= Marked_if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y))) ;
  Marked_if(true,X,Y) >= Marked_activate(X) ;
  Marked_if(false,X,Y) >= Marked_activate(Y) ;
 }
 + Disjunctions:{ 
{
  Marked_activate(n__s(X)) > Marked_activate(X) ;
 }
{
  Marked_activate(n__diff(X1,X2)) > Marked_activate(X1) ;
 }
{
  Marked_activate(n__diff(X1,X2)) > Marked_activate(X2) ;
 }
{
  Marked_activate(n__diff(X1,X2)) > Marked_diff(activate(X1),activate(X2)) ;
 }
{
  Marked_activate(n__p(X)) > Marked_activate(X) ;
 }
{
  Marked_diff(X,Y) > Marked_if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y))) ;
 }
{
  Marked_if(true,X,Y) > Marked_activate(X) ;
 }
{
  Marked_if(false,X,Y) > Marked_activate(Y) ;
 }
 } 
=== 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: 0 >= n__0
constraint: p(0) >= 0
constraint: p(s(X)) >= X
constraint: p(X) >= n__p(X)
constraint: s(X) >= n__s(X)
constraint: leq(0,Y) >= true
constraint: leq(s(X),0) >= false
constraint: leq(s(X),s(Y)) >= leq(X,Y)
constraint: activate(n__0) >= 0
constraint: activate(n__s(X)) >= s(activate(X))
constraint: activate(n__diff(X1,X2)) >= diff(activate(X1),activate(X2))
constraint: activate(n__p(X)) >= p(activate(X))
constraint: activate(X) >= X
constraint: if(true,X,Y) >= activate(X)
constraint: if(false,X,Y) >= activate(Y)
constraint: diff(X,Y) >= if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y)))
constraint: diff(X1,X2) >= n__diff(X1,X2)
constraint: Marked_activate(n__s(X)) >= Marked_activate(X)
constraint: Marked_activate(n__diff(X1,X2)) >= Marked_activate(X1)
constraint: Marked_activate(n__diff(X1,X2)) >= Marked_activate(X2)
constraint: Marked_activate(n__diff(X1,X2)) >= Marked_diff(activate(X1),
                                                activate(X2))
constraint: Marked_activate(n__p(X)) >= Marked_activate(X)
constraint: Marked_diff(X,Y) >= Marked_if(leq(X,Y),n__0,
                                 n__s(n__diff(n__p(X),Y)))
constraint: Marked_if(true,X,Y) >= Marked_activate(X)
constraint: Marked_if(false,X,Y) >= Marked_activate(Y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  0 >= n__0 ;
  p(0) >= 0 ;
  p(s(X)) >= X ;
  p(X) >= n__p(X) ;
  s(X) >= n__s(X) ;
  leq(0,Y) >= true ;
  leq(s(X),0) >= false ;
  leq(s(X),s(Y)) >= leq(X,Y) ;
  activate(n__0) >= 0 ;
  activate(n__s(X)) >= s(activate(X)) ;
  activate(n__diff(X1,X2)) >= diff(activate(X1),activate(X2)) ;
  activate(n__p(X)) >= p(activate(X)) ;
  activate(X) >= X ;
  if(true,X,Y) >= activate(X) ;
  if(false,X,Y) >= activate(Y) ;
  diff(X,Y) >= if(leq(X,Y),n__0,n__s(n__diff(n__p(X),Y))) ;
  diff(X1,X2) >= n__diff(X1,X2) ;
  Marked_leq(s(X),s(Y)) >= Marked_leq(X,Y) ;
 }
 + Disjunctions:{ 
{
  Marked_leq(s(X),s(Y)) > Marked_leq(X,Y) ;
 }
 } 
=== 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 5.787972 seconds (real time)
Cime Exit Status: 0