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

TRS termination of:
[1] perfectp(0) -> false
[2] perfectp(s(x)) -> f(x,s(0),s(x),s(x))
[3] f(0,y,0,u) -> true
[4] f(0,y,s(z),u) -> false
[5] f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
[6] f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))


Sub problem: 
guided: 

DP termination of:
<Marked_perfectp(s(x)) , Marked_f(x,s(0),s(x),s(x))>
<Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
<Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
<Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)> 
      --> <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
  <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)> 
     --> <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
  <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)> 
     --> <Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
  <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)> 
     --> <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] perfectp(0) -> false
[2] perfectp(s(x)) -> f(x,s(0),s(x),s(x))
[3] f(0,y,0,u) -> true
[4] f(0,y,s(z),u) -> false
[5] f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
[6] f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_perfectp(s(x)) , Marked_f(x,s(0),s(x),s(x))>
<Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
<Marked_f(s(x),s(y),z,u) , Marked_f(s(x),minus(y,x),z,u)>
<Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(x),0,z,u) , Marked_f(x,u,minus(z,s(x)),u)>
<Marked_f(s(x),s(y),z,u) , Marked_f(x,u,z,u)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.007395 seconds (real time)
Cime Exit Status: 0