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

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


Sub problem: 
guided: 

DP termination of:
<Marked_sqr(s(x)) , Marked_+(sqr(x),s(double(x)))>
<Marked_sqr(s(x)) , Marked_sqr(x)>
<Marked_sqr(s(x)) , Marked_double(x)>
<Marked_double(s(x)) , Marked_double(x)>
<Marked_+(x,s(y)) , Marked_+(x,y)>
<Marked_sqr(s(x)) , Marked_+(sqr(x),double(x))>
<Marked_sqr(s(x)) , Marked_sqr(x)>
<Marked_sqr(s(x)) , Marked_double(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

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

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

{  <Marked_double(s(x)) , Marked_double(x)> 
      --> <Marked_double(s(x)) , Marked_double(x)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_sqr -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_double -> 1

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

Cime worked for 0.009164 seconds (real time)
Cime Exit Status: 0