- : unit = ()
- : 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) -> X
[7] if(false,X,Y) -> Y
[8] diff(X,Y) -> if(leq(X,Y),0,s(diff(p(X),Y)))


Sub problem: 
guided: 

DP termination of:
<Marked_leq(s(X),s(Y)) , Marked_leq(X,Y)>
<Marked_diff(X,Y) , Marked_if(leq(X,Y),0,s(diff(p(X),Y)))>
<Marked_diff(X,Y) , Marked_leq(X,Y)>
<Marked_diff(X,Y) , Marked_diff(p(X),Y)>
<Marked_diff(X,Y) , Marked_p(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_diff(X,Y) , Marked_diff(p(X),Y)> 
      --> <Marked_diff(X,Y) , Marked_diff(p(X),Y)>
}

{  <Marked_leq(s(X),s(Y)) , Marked_leq(X,Y)> 
      --> <Marked_leq(s(X),s(Y)) , Marked_leq(X,Y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  p(0) >= 0 ;
  p(s(X)) >= X ;
  leq(0,Y) >= true ;
  leq(s(X),0) >= false ;
  leq(s(X),s(Y)) >= leq(X,Y) ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  diff(X,Y) >= if(leq(X,Y),0,s(diff(p(X),Y))) ;
  Marked_diff(X,Y) >= Marked_diff(p(X),Y) ;
 }
 + Disjunctions:{ 
{
  Marked_diff(X,Y) > Marked_diff(p(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 (Simple graph)
Found the following constraints:
{
  p(0) >= 0 ;
  p(s(X)) >= X ;
  leq(0,Y) >= true ;
  leq(s(X),0) >= false ;
  leq(s(X),s(Y)) >= leq(X,Y) ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  diff(X,Y) >= if(leq(X,Y),0,s(diff(p(X),Y))) ;
  Marked_diff(X,Y) > Marked_diff(p(X),Y) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  p(0) >= 0 ;
  p(s(X)) >= X ;
  leq(0,Y) >= true ;
  leq(s(X),0) >= false ;
  leq(s(X),s(Y)) >= leq(X,Y) ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  diff(X,Y) >= if(leq(X,Y),0,s(diff(p(X),Y))) ;
  Marked_diff(X,Y) > Marked_diff(p(X),Y) ;
 }
 + Disjunctions:{ 
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
=== 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 ===
No solution found for these parameters.(31 bt (36) [9])
=== TIMER virtual : 15.000000 ===
Entering poly_solver
=== 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
=== 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 0.615214 seconds (real time)
Cime Exit Status: 0