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

TRS termination of:
[1] prime(0) -> false
[2] prime(s(0)) -> false
[3] prime(s(s(x))) -> prime1(s(s(x)),s(x))
[4] prime1(x,0) -> false
[5] prime1(x,s(0)) -> true
[6] prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
[7] divp(x,y) -> =(rem(x,y),0)


Sub problem: 
guided: 

DP termination of:
<Marked_prime(s(s(x))) , Marked_prime1(s(s(x)),s(x))>
<Marked_prime1(x,s(s(y))) , Marked_divp(s(s(y)),x)>
<Marked_prime1(x,s(s(y))) , Marked_prime1(x,s(y))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_prime1(x,s(s(y))) , Marked_prime1(x,s(y))> 
      --> <Marked_prime1(x,s(s(y))) , Marked_prime1(x,s(y))>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  prime(0) >= false ;
  prime(s(0)) >= false ;
  prime(s(s(x))) >= prime1(s(s(x)),s(x)) ;
  prime1(x,0) >= false ;
  prime1(x,s(0)) >= true ;
  prime1(x,s(s(y))) >= and(not(divp(s(s(y)),x)),prime1(x,s(y))) ;
  divp(x,y) >= =(rem(x,y),0) ;
  Marked_prime1(x,s(s(y))) >= Marked_prime1(x,s(y)) ;
 }
 + Disjunctions:{ 
{
  Marked_prime1(x,s(s(y))) > Marked_prime1(x,s(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: prime(0) >= false
constraint: prime(s(0)) >= false
constraint: prime(s(s(x))) >= prime1(s(s(x)),s(x))
constraint: prime1(x,0) >= false
constraint: prime1(x,s(0)) >= true
constraint: prime1(x,s(s(y))) >= and(not(divp(s(s(y)),x)),prime1(x,s(y)))
constraint: divp(x,y) >= =(rem(x,y),0)
constraint: Marked_prime1(x,s(s(y))) >= Marked_prime1(x,s(y))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] prime(0) -> false
[2] prime(s(0)) -> false
[3] prime(s(s(x))) -> prime1(s(s(x)),s(x))
[4] prime1(x,0) -> false
[5] prime1(x,s(0)) -> true
[6] prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
[7] divp(x,y) -> =(rem(x,y),0)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_prime(s(s(x))) , Marked_prime1(s(s(x)),s(x))>
<Marked_prime1(x,s(s(y))) , Marked_divp(s(s(y)),x)>
<Marked_prime1(x,s(s(y))) , Marked_prime1(x,s(y))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_prime1(x,s(s(y))) , Marked_prime1(x,s(y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ false ] () = 0; 
 [ divp ] (X0,X1) = 0; 
 [ prime1 ] (X0,X1) = 0; 
 [ Marked_prime1 ] (X0,X1) = 3*X1 + 0; 
 [ 0 ] () = 0; 
 [ rem ] (X0,X1) = 3*X0 + 3*X1 + 0; 
 [ and ] (X0,X1) = 0; 
 [ prime ] (X0) = 2 + 0; 
 [ = ] (X0,X1) = 0; 
 [ true ] () = 0; 
 [ s ] (X0) = 1 + 3*X0 + 0; 
 [ not ] (X0) = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.072296 seconds (real time)
Cime Exit Status: 0