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

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


Sub problem: 
guided: 

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

{  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , Marked_f(x)>
  <Marked_f(s(x)) , Marked_f(x)> --> <Marked_f(s(x)) , 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) -> 1
[2] f(s(x)) -> g(f(x))
[3] g(x) -> +(x,s(x))
[4] f(s(x)) -> +(f(x),s(f(x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(x)) , Marked_g(f(x))>
<Marked_f(s(x)) , Marked_f(x)>
<Marked_f(s(x)) , Marked_f(x)>
<Marked_f(s(x)) , Marked_f(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(s(x)) , Marked_f(x)>
<Marked_f(s(x)) , Marked_f(x)>
<Marked_f(s(x)) , Marked_f(x)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.004806 seconds (real time)
Cime Exit Status: 0