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

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


Sub problem: 
guided: 

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

{  <Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))> 
      --> <Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))>
  <Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))> 
     --> <Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))>
  <Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))> 
     --> <Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))>
  <Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))> 
     --> <Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))>
}

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

ST: Marked_g -> 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] f(0) -> 1
[2] f(s(x)) -> g(x,s(x))
[3] g(0,y) -> y
[4] g(s(x),y) -> g(x,+(y,s(x)))
[5] +(x,0) -> x
[6] +(x,s(y)) -> s(+(x,y))
[7] g(s(x),y) -> g(x,s(+(y,x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(s(x)) , Marked_g(x,s(x))>
<Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))>
<Marked_g(s(x),y) , Marked_+(y,s(x))>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_g(s(x),y) , Marked_g(x,s(+(y,x)))>
<Marked_g(s(x),y) , Marked_+(y,x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_g(s(x),y) , Marked_g(x,+(y,s(x)))>
<Marked_g(s(x),y) , Marked_g(x,s(+(y,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 0.007438 seconds (real time)
Cime Exit Status: 0