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

TRS termination of:
[1] f(0) -> s(0)
[2] f(s(0)) -> s(s(0))
[3] f(s(0)) ->  *(s(s(0)),f(0))
[4] f(+(x,s(0))) -> +(s(s(0)),f(x))
[5] f(+(x,y)) ->  *(f(x),f(y))


Sub problem: 
guided: 

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

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

ST: Marked_f -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(0) -> s(0)
[2] f(s(0)) -> s(s(0))
[3] f(s(0)) ->  *(s(s(0)),f(0))
[4] f(+(x,s(0))) -> +(s(s(0)),f(x))
[5] f(+(x,y)) ->  *(f(x),f(y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(0)) , Marked_f(0)>
<Marked_f(+(x,s(0))) , Marked_f(x)>
<Marked_f(+(x,y)) , Marked_f(x)>
<Marked_f(+(x,y)) , Marked_f(y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(+(x,s(0))) , Marked_f(x)>
<Marked_f(+(x,y)) , Marked_f(x)>
<Marked_f(+(x,y)) , Marked_f(y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.005323 seconds (real time)
Cime Exit Status: 0