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

TRS termination of:
[1] sort(nil) -> nil
[2] sort(cons(x,y)) -> insert(x,sort(y))
[3] insert(x,nil) -> cons(x,nil)
[4] insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
[5] choose(x,cons(v,w),y,0) -> cons(x,cons(v,w))
[6] choose(x,cons(v,w),0,s(z)) -> cons(v,insert(x,w))
[7] choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)


Sub problem: 
guided: 

DP termination of:
<Marked_sort(cons(x,y)) , Marked_insert(x,sort(y))>
<Marked_sort(cons(x,y)) , Marked_sort(y)>
<Marked_insert(x,cons(v,w)) , Marked_choose(x,cons(v,w),x,v)>
<Marked_choose(x,cons(v,w),0,s(z)) , Marked_insert(x,w)>
<Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_sort(cons(x,y)) , Marked_sort(y)> 
      --> <Marked_sort(cons(x,y)) , Marked_sort(y)>
}

{  <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)> 
      --> <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),
                                                   y,z)>
  <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)> 
     --> <Marked_choose(x,cons(v,w),0,s(z)) , Marked_insert(x,w)>
  <Marked_choose(x,cons(v,w),0,s(z)) , Marked_insert(x,w)> 
     --> <Marked_insert(x,cons(v,w)) , Marked_choose(x,cons(v,w),x,v)>
  <Marked_insert(x,cons(v,w)) , Marked_choose(x,cons(v,w),x,v)> 
     --> <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)>
  <Marked_insert(x,cons(v,w)) , Marked_choose(x,cons(v,w),x,v)> 
     --> <Marked_choose(x,cons(v,w),0,s(z)) , Marked_insert(x,w)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_sort -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_choose -> 2
Marked_insert -> 2

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

{  <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)> 
      --> <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),
                                                   y,z)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_choose -> 3

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] sort(nil) -> nil
[2] sort(cons(x,y)) -> insert(x,sort(y))
[3] insert(x,nil) -> cons(x,nil)
[4] insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
[5] choose(x,cons(v,w),y,0) -> cons(x,cons(v,w))
[6] choose(x,cons(v,w),0,s(z)) -> cons(v,insert(x,w))
[7] choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_sort(cons(x,y)) , Marked_insert(x,sort(y))>
<Marked_sort(cons(x,y)) , Marked_sort(y)>
<Marked_insert(x,cons(v,w)) , Marked_choose(x,cons(v,w),x,v)>
<Marked_choose(x,cons(v,w),0,s(z)) , Marked_insert(x,w)>
<Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sort(cons(x,y)) , Marked_sort(y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_insert(x,cons(v,w)) , Marked_choose(x,cons(v,w),x,v)>
<Marked_choose(x,cons(v,w),0,s(z)) , Marked_insert(x,w)>
<Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)>
<Marked_insert(x,cons(v,w)) , Marked_choose(x,cons(v,w),x,v)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.012954 seconds (real time)
Cime Exit Status: 0