- : unit = ()
- : 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 (Subterm criterion)

ST: Marked_prime1 -> 2

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: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.004062 seconds (real time)
Cime Exit Status: 0