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

TRS termination of:
[1] qsort(nil) -> nil
[2] qsort(.(x,y)) -> ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
[3] lowers(x,nil) -> nil
[4] lowers(x,.(y,z)) -> if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
[5] greaters(x,nil) -> nil
[6] greaters(x,.(y,z)) -> if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))


Sub problem: 
guided: 

DP termination of:
<Marked_qsort(.(x,y)) , Marked_qsort(lowers(x,y))>
<Marked_qsort(.(x,y)) , Marked_lowers(x,y)>
<Marked_qsort(.(x,y)) , Marked_qsort(greaters(x,y))>
<Marked_qsort(.(x,y)) , Marked_greaters(x,y)>
<Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
<Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
<Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
<Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_qsort(.(x,y)) , Marked_qsort(greaters(x,y))> 
      --> <Marked_qsort(.(x,y)) , Marked_qsort(greaters(x,y))>
  <Marked_qsort(.(x,y)) , Marked_qsort(greaters(x,y))> 
     --> <Marked_qsort(.(x,y)) , Marked_qsort(lowers(x,y))>
  <Marked_qsort(.(x,y)) , Marked_qsort(lowers(x,y))> 
     --> <Marked_qsort(.(x,y)) , Marked_qsort(greaters(x,y))>
  <Marked_qsort(.(x,y)) , Marked_qsort(lowers(x,y))> 
     --> <Marked_qsort(.(x,y)) , Marked_qsort(lowers(x,y))>
}

{  <Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)> 
      --> <Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
  <Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)> 
     --> <Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
  <Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)> 
     --> <Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
  <Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)> 
     --> <Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
}

{  <Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)> 
      --> <Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
  <Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)> 
     --> <Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
  <Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)> 
     --> <Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
  <Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)> 
     --> <Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  qsort(nil) >= nil ;
  qsort(.(x,y)) >= ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y)))) ;
  lowers(x,nil) >= nil ;
  lowers(x,.(y,z)) >= if(<=(y,x),.(y,lowers(x,z)),lowers(x,z)) ;
  greaters(x,nil) >= nil ;
  greaters(x,.(y,z)) >= if(<=(y,x),greaters(x,z),.(y,greaters(x,z))) ;
  Marked_qsort(.(x,y)) >= Marked_qsort(lowers(x,y)) ;
  Marked_qsort(.(x,y)) >= Marked_qsort(greaters(x,y)) ;
 }
 + Disjunctions:{ 
{
  Marked_qsort(.(x,y)) > Marked_qsort(lowers(x,y)) ;
 }
{
  Marked_qsort(.(x,y)) > Marked_qsort(greaters(x,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: qsort(nil) >= nil
constraint: qsort(.(x,y)) >= ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
constraint: lowers(x,nil) >= nil
constraint: lowers(x,.(y,z)) >= if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
constraint: greaters(x,nil) >= nil
constraint: greaters(x,.(y,z)) >= if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
constraint: Marked_qsort(.(x,y)) >= Marked_qsort(lowers(x,y))
constraint: Marked_qsort(.(x,y)) >= Marked_qsort(greaters(x,y))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  qsort(nil) >= nil ;
  qsort(.(x,y)) >= ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y)))) ;
  lowers(x,nil) >= nil ;
  lowers(x,.(y,z)) >= if(<=(y,x),.(y,lowers(x,z)),lowers(x,z)) ;
  greaters(x,nil) >= nil ;
  greaters(x,.(y,z)) >= if(<=(y,x),greaters(x,z),.(y,greaters(x,z))) ;
  Marked_lowers(x,.(y,z)) >= Marked_lowers(x,z) ;
 }
 + Disjunctions:{ 
{
  Marked_lowers(x,.(y,z)) > Marked_lowers(x,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: qsort(nil) >= nil
constraint: qsort(.(x,y)) >= ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
constraint: lowers(x,nil) >= nil
constraint: lowers(x,.(y,z)) >= if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
constraint: greaters(x,nil) >= nil
constraint: greaters(x,.(y,z)) >= if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
constraint: Marked_lowers(x,.(y,z)) >= Marked_lowers(x,z)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  qsort(nil) >= nil ;
  qsort(.(x,y)) >= ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y)))) ;
  lowers(x,nil) >= nil ;
  lowers(x,.(y,z)) >= if(<=(y,x),.(y,lowers(x,z)),lowers(x,z)) ;
  greaters(x,nil) >= nil ;
  greaters(x,.(y,z)) >= if(<=(y,x),greaters(x,z),.(y,greaters(x,z))) ;
  Marked_greaters(x,.(y,z)) >= Marked_greaters(x,z) ;
 }
 + Disjunctions:{ 
{
  Marked_greaters(x,.(y,z)) > Marked_greaters(x,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: qsort(nil) >= nil
constraint: qsort(.(x,y)) >= ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
constraint: lowers(x,nil) >= nil
constraint: lowers(x,.(y,z)) >= if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
constraint: greaters(x,nil) >= nil
constraint: greaters(x,.(y,z)) >= if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
constraint: Marked_greaters(x,.(y,z)) >= Marked_greaters(x,z)
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] qsort(nil) -> nil
[2] qsort(.(x,y)) -> ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
[3] lowers(x,nil) -> nil
[4] lowers(x,.(y,z)) -> if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
[5] greaters(x,nil) -> nil
[6] greaters(x,.(y,z)) -> if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_qsort(.(x,y)) , Marked_qsort(lowers(x,y))>
<Marked_qsort(.(x,y)) , Marked_lowers(x,y)>
<Marked_qsort(.(x,y)) , Marked_qsort(greaters(x,y))>
<Marked_qsort(.(x,y)) , Marked_greaters(x,y)>
<Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
<Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
<Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
<Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_qsort(.(x,y)) , Marked_qsort(lowers(x,y))>
<Marked_qsort(.(x,y)) , Marked_qsort(greaters(x,y))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ . ] (X0,X1) = 2 + 2*X0 + 3*X1 + 0; 
 [ ++ ] (X0,X1) = 2 + 0; 
 [ Marked_qsort ] (X0) = 3*X0 + 0; 
 [ if ] (X0,X1,X2) = 0; 
 [ qsort ] (X0) = 2 + 3*X0 + 0; 
 [ greaters ] (X0,X1) = 0; 
 [ lowers ] (X0,X1) = 3*X1 + 0; 
 [ <= ] (X0,X1) = 0; 
 ]} 
{
 
DP termination of:
<Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
<Marked_lowers(x,.(y,z)) , Marked_lowers(x,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ . ] (X0,X1) = 1 + 2*X1 + 0; 
 [ ++ ] (X0,X1) = 0; 
 [ if ] (X0,X1,X2) = 0; 
 [ qsort ] (X0) = 0; 
 [ Marked_lowers ] (X0,X1) = 3*X1 + 0; 
 [ greaters ] (X0,X1) = 0; 
 [ lowers ] (X0,X1) = 0; 
 [ <= ] (X0,X1) = 0; 
 ]} 
{
 
DP termination of:
<Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
<Marked_greaters(x,.(y,z)) , Marked_greaters(x,z)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ nil ] () = 0; 
 [ Marked_greaters ] (X0,X1) = 3*X1 + 0; 
 [ . ] (X0,X1) = 1 + 1*X1 + 0; 
 [ ++ ] (X0,X1) = 0; 
 [ if ] (X0,X1,X2) = 0; 
 [ qsort ] (X0) = 0; 
 [ greaters ] (X0,X1) = 0; 
 [ lowers ] (X0,X1) = 0; 
 [ <= ] (X0,X1) = 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.217504 seconds (real time)
Cime Exit Status: 0