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

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


Sub problem: 
guided: 

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

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

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

ST: Marked_double -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

ST: Marked_+ -> 1

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

Cime worked for 0.009242 seconds (real time)
Cime Exit Status: 0