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

TRS termination of:
[1] primes -> sieve(from(s(s(0))))
[2] from(X) -> cons(X,from(s(X)))
[3] head(cons(X,Y)) -> X
[4] tail(cons(X,Y)) -> Y
[5] if(true,X,Y) -> X
[6] if(false,X,Y) -> Y
[7] filter(s(s(X)),cons(Y,Z)) ->
 if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))
[8] sieve(cons(X,Y)) -> cons(X,filter(X,sieve(Y)))


Sub problem: 
guided: 

DP termination of:
<Marked_primes , Marked_sieve(from(s(s(0))))>
<Marked_primes , Marked_from(s(s(0)))>
<Marked_from(X) , Marked_from(s(X))>
<Marked_filter(s(s(X)),cons(Y,Z)) , Marked_if(divides(s(s(X)),Y),
                                     filter(s(s(X)),Z),
                                     cons(Y,filter(X,sieve(Y))))>
<Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(s(s(X)),Z)>
<Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(X,sieve(Y))>
<Marked_filter(s(s(X)),cons(Y,Z)) , Marked_sieve(Y)>
<Marked_sieve(cons(X,Y)) , Marked_filter(X,sieve(Y))>
<Marked_sieve(cons(X,Y)) , Marked_sieve(Y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_from(X) , Marked_from(s(X))> 
      --> <Marked_from(X) , Marked_from(s(X))>
}

{  <Marked_sieve(cons(X,Y)) , Marked_sieve(Y)> 
      --> <Marked_sieve(cons(X,Y)) , Marked_sieve(Y)>
  <Marked_sieve(cons(X,Y)) , Marked_sieve(Y)> 
     --> <Marked_sieve(cons(X,Y)) , Marked_filter(X,sieve(Y))>
  <Marked_sieve(cons(X,Y)) , Marked_filter(X,sieve(Y))> 
     --> <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_sieve(Y)>
  <Marked_sieve(cons(X,Y)) , Marked_filter(X,sieve(Y))> 
     --> <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(X,sieve(Y))>
  <Marked_sieve(cons(X,Y)) , Marked_filter(X,sieve(Y))> 
     --> <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(s(s(X)),Z)>
  <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_sieve(Y)> 
     --> <Marked_sieve(cons(X,Y)) , Marked_sieve(Y)>
  <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_sieve(Y)> 
     --> <Marked_sieve(cons(X,Y)) , Marked_filter(X,sieve(Y))>
  <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(X,sieve(Y))> 
     --> <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_sieve(Y)>
  <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(X,sieve(Y))> 
     --> <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(X,sieve(Y))>
  <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(X,sieve(Y))> 
     --> <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(s(s(X)),Z)>
  <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(s(s(X)),Z)> 
     --> <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_sieve(Y)>
  <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(s(s(X)),Z)> 
     --> <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(X,sieve(Y))>
  <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(s(s(X)),Z)> 
     --> <Marked_filter(s(s(X)),cons(Y,Z)) , Marked_filter(s(s(X)),Z)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sieve(cons(X,Y)) >= cons(X,filter(X,sieve(Y))) ;
  from(X) >= cons(X,from(s(X))) ;
  primes >= sieve(from(s(s(0)))) ;
  head(cons(X,Y)) >= X ;
  tail(cons(X,Y)) >= Y ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  filter(s(s(X)),cons(Y,Z)) >= if(divides(s(s(X)),Y),filter(s(s(X)),Z),
                                cons(Y,filter(X,sieve(Y)))) ;
  Marked_from(X) >= Marked_from(s(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_from(X) > Marked_from(s(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
=== 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:
{
  sieve(cons(X,Y)) >= cons(X,filter(X,sieve(Y))) ;
  from(X) >= cons(X,from(s(X))) ;
  primes >= sieve(from(s(s(0)))) ;
  head(cons(X,Y)) >= X ;
  tail(cons(X,Y)) >= Y ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  filter(s(s(X)),cons(Y,Z)) >= if(divides(s(s(X)),Y),filter(s(s(X)),Z),
                                cons(Y,filter(X,sieve(Y)))) ;
  Marked_from(X) > Marked_from(s(X)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  sieve(cons(X,Y)) >= cons(X,filter(X,sieve(Y))) ;
  from(X) >= cons(X,from(s(X))) ;
  primes >= sieve(from(s(s(0)))) ;
  head(cons(X,Y)) >= X ;
  tail(cons(X,Y)) >= Y ;
  if(true,X,Y) >= X ;
  if(false,X,Y) >= Y ;
  filter(s(s(X)),cons(Y,Z)) >= if(divides(s(s(X)),Y),filter(s(s(X)),Z),
                                cons(Y,filter(X,sieve(Y)))) ;
  Marked_from(X) > Marked_from(s(X)) ;
 }
 + 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.(82 bt (120) [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 8.023360 seconds (real time)
Cime Exit Status: 0