- : 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 (Choosing graph)
Trying to solve the following constraints:
{
  sort(nil) >= nil ;
  sort(cons(x,y)) >= insert(x,sort(y)) ;
  insert(x,nil) >= cons(x,nil) ;
  insert(x,cons(v,w)) >= choose(x,cons(v,w),x,v) ;
  choose(x,cons(v,w),0,s(z)) >= cons(v,insert(x,w)) ;
  choose(x,cons(v,w),s(y),s(z)) >= choose(x,cons(v,w),y,z) ;
  choose(x,cons(v,w),y,0) >= cons(x,cons(v,w)) ;
  Marked_sort(cons(x,y)) >= Marked_sort(y) ;
 }
 + Disjunctions:{ 
{
  Marked_sort(cons(x,y)) > Marked_sort(y) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: sort(nil) >= nil
constraint: sort(cons(x,y)) >= insert(x,sort(y))
constraint: insert(x,nil) >= cons(x,nil)
constraint: insert(x,cons(v,w)) >= choose(x,cons(v,w),x,v)
constraint: choose(x,cons(v,w),0,s(z)) >= cons(v,insert(x,w))
constraint: choose(x,cons(v,w),s(y),s(z)) >= choose(x,cons(v,w),y,z)
constraint: choose(x,cons(v,w),y,0) >= cons(x,cons(v,w))
constraint: Marked_sort(cons(x,y)) >= Marked_sort(y)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  sort(nil) >= nil ;
  sort(cons(x,y)) >= insert(x,sort(y)) ;
  insert(x,nil) >= cons(x,nil) ;
  insert(x,cons(v,w)) >= choose(x,cons(v,w),x,v) ;
  choose(x,cons(v,w),0,s(z)) >= cons(v,insert(x,w)) ;
  choose(x,cons(v,w),s(y),s(z)) >= choose(x,cons(v,w),y,z) ;
  choose(x,cons(v,w),y,0) >= cons(x,cons(v,w)) ;
  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) ;
  Marked_insert(x,cons(v,w)) >= Marked_choose(x,cons(v,w),x,v) ;
 }
 + Disjunctions:{ 
{
  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) ;
 }
{
  Marked_insert(x,cons(v,w)) > Marked_choose(x,cons(v,w),x,v) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: sort(nil) >= nil
constraint: sort(cons(x,y)) >= insert(x,sort(y))
constraint: insert(x,nil) >= cons(x,nil)
constraint: insert(x,cons(v,w)) >= choose(x,cons(v,w),x,v)
constraint: choose(x,cons(v,w),0,s(z)) >= cons(v,insert(x,w))
constraint: choose(x,cons(v,w),s(y),s(z)) >= choose(x,cons(v,w),y,z)
constraint: choose(x,cons(v,w),y,0) >= cons(x,cons(v,w))
constraint: Marked_choose(x,cons(v,w),0,s(z)) >= Marked_insert(x,w)
constraint: Marked_choose(x,cons(v,w),s(y),s(z)) >= Marked_choose(x,cons(v,w),
                                                     y,z)
constraint: Marked_insert(x,cons(v,w)) >= Marked_choose(x,cons(v,w),x,v)
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 (Choosing graph)
Trying to solve the following constraints:
{
  sort(nil) >= nil ;
  sort(cons(x,y)) >= insert(x,sort(y)) ;
  insert(x,nil) >= cons(x,nil) ;
  insert(x,cons(v,w)) >= choose(x,cons(v,w),x,v) ;
  choose(x,cons(v,w),0,s(z)) >= cons(v,insert(x,w)) ;
  choose(x,cons(v,w),s(y),s(z)) >= choose(x,cons(v,w),y,z) ;
  choose(x,cons(v,w),y,0) >= cons(x,cons(v,w)) ;
  Marked_choose(x,cons(v,w),s(y),s(z)) >= Marked_choose(x,cons(v,w),y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_choose(x,cons(v,w),s(y),s(z)) > Marked_choose(x,cons(v,w),y,z) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: sort(nil) >= nil
constraint: sort(cons(x,y)) >= insert(x,sort(y))
constraint: insert(x,nil) >= cons(x,nil)
constraint: insert(x,cons(v,w)) >= choose(x,cons(v,w),x,v)
constraint: choose(x,cons(v,w),0,s(z)) >= cons(v,insert(x,w))
constraint: choose(x,cons(v,w),s(y),s(z)) >= choose(x,cons(v,w),y,z)
constraint: choose(x,cons(v,w),y,0) >= cons(x,cons(v,w))
constraint: Marked_choose(x,cons(v,w),s(y),s(z)) >= Marked_choose(x,cons(v,w),
                                                     y,z)
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: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ choose ] (X0,X1,X2,X3) = 2 + 1*X1 + 0; 
 [ insert ] (X0,X1) = 2 + 1*X1 + 0; 
 [ s ] (X0) = 3*X0 + 0; 
 [ sort ] (X0) = 1*X0 + 0; 
 [ Marked_sort ] (X0) = 3*X0 + 0; 
 [ 0 ] () = 0; 
 [ cons ] (X0,X1) = 2 + 1*X1 + 0; 
 ]} 
{
 
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: CG using polynomial interpretation = 
 [ nil ] () = 3; 
 [ Marked_insert ] (X0,X1) = 3*X1 + 3*X0 + 1; 
 [ choose ] (X0,X1,X2,X3) = 1*X1 + 3; 
 [ insert ] (X0,X1) = 1*X1 + 3; 
 [ s ] (X0) = 3*X0; 
 [ sort ] (X0) = 3*X0; 
 [ 0 ] () = 0; 
 [ cons ] (X0,X1) = 1*X1 + 1; 
 [ Marked_choose ] (X0,X1,X2,X3) = 3*X1 + 3*X0; 
 removing <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)>
 [ {
      
     DP termination of:
     <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_choose(x,cons(v,w),s(y),s(z)) , Marked_choose(x,cons(v,w),y,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ choose ] (X0,X1,X2,X3) = 0; 
 [ insert ] (X0,X1) = 0; 
 [ s ] (X0) = 1 + 3*X0 + 0; 
 [ sort ] (X0) = 0; 
 [ 0 ] () = 0; 
 [ cons ] (X0,X1) = 0; 
 [ Marked_choose ] (X0,X1,X2,X3) = 1*X3 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.126881 seconds (real time)
Cime Exit Status: 0