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

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


Sub problem: 
guided: 

DP termination of:
<Marked_fib(s(s(x))) , Marked_+(fib(s(x)),fib(x))>
<Marked_fib(s(s(x))) , Marked_fib(s(x))>
<Marked_fib(s(s(x))) , Marked_fib(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_fib(s(s(x))) , Marked_fib(x)> 
      --> <Marked_fib(s(s(x))) , Marked_fib(x)>
  <Marked_fib(s(s(x))) , Marked_fib(x)> 
     --> <Marked_fib(s(s(x))) , Marked_fib(s(x))>
  <Marked_fib(s(s(x))) , Marked_fib(s(x))> 
     --> <Marked_fib(s(s(x))) , Marked_fib(x)>
  <Marked_fib(s(s(x))) , Marked_fib(s(x))> 
     --> <Marked_fib(s(s(x))) , Marked_fib(s(x))>
}

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

ST: Marked_fib -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 2

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

Cime worked for 0.006322 seconds (real time)
Cime Exit Status: 0