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

TRS termination of:
[1] bsort(nil) -> nil
[2] bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y))))))
[3] bubble(nil) -> nil
[4] bubble(.(x,nil)) -> .(x,nil)
[5] bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z))))
[6] last(nil) -> 0
[7] last(.(x,nil)) -> x
[8] last(.(x,.(y,z))) -> last(.(y,z))
[9] butlast(nil) -> nil
[10] butlast(.(x,nil)) -> nil
[11] butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z)))


Sub problem: 
guided: 

DP termination of:
<Marked_bsort(.(x,y)) , Marked_last(.(bubble(.(x,y)),
                                     bsort(butlast(bubble(.(x,y))))))>
<Marked_bsort(.(x,y)) , Marked_bubble(.(x,y))>
<Marked_bsort(.(x,y)) , Marked_bsort(butlast(bubble(.(x,y))))>
<Marked_bsort(.(x,y)) , Marked_butlast(bubble(.(x,y)))>
<Marked_bsort(.(x,y)) , Marked_bubble(.(x,y))>
<Marked_bubble(.(x,.(y,z))) , Marked_bubble(.(x,z))>
<Marked_bubble(.(x,.(y,z))) , Marked_bubble(.(y,z))>
<Marked_last(.(x,.(y,z))) , Marked_last(.(y,z))>
<Marked_butlast(.(x,.(y,z))) , Marked_butlast(.(y,z))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_bsort(.(x,y)) , Marked_bsort(butlast(bubble(.(x,y))))> 
      --> <Marked_bsort(.(x,y)) , Marked_bsort(butlast(bubble(.(x,y))))>
}

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

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

{  <Marked_butlast(.(x,.(y,z))) , Marked_butlast(.(y,z))> 
      --> <Marked_butlast(.(x,.(y,z))) , Marked_butlast(.(y,z))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  bsort(nil) >= nil ;
  bsort(.(x,y)) >= last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y)))))) ;
  last(nil) >= 0 ;
  last(.(x,nil)) >= x ;
  last(.(x,.(y,z))) >= last(.(y,z)) ;
  bubble(nil) >= nil ;
  bubble(.(x,nil)) >= .(x,nil) ;
  bubble(.(x,.(y,z))) >= if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z)))) ;
  butlast(nil) >= nil ;
  butlast(.(x,nil)) >= nil ;
  butlast(.(x,.(y,z))) >= .(x,butlast(.(y,z))) ;
  Marked_bsort(.(x,y)) >= Marked_bsort(butlast(bubble(.(x,y)))) ;
 }
 + Disjunctions:{ 
{
  Marked_bsort(.(x,y)) > Marked_bsort(butlast(bubble(.(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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  bsort(nil) >= nil ;
  bsort(.(x,y)) >= last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y)))))) ;
  last(nil) >= 0 ;
  last(.(x,nil)) >= x ;
  last(.(x,.(y,z))) >= last(.(y,z)) ;
  bubble(nil) >= nil ;
  bubble(.(x,nil)) >= .(x,nil) ;
  bubble(.(x,.(y,z))) >= if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z)))) ;
  butlast(nil) >= nil ;
  butlast(.(x,nil)) >= nil ;
  butlast(.(x,.(y,z))) >= .(x,butlast(.(y,z))) ;
  Marked_bsort(.(x,y)) > Marked_bsort(butlast(bubble(.(x,y)))) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  bsort(nil) >= nil ;
  bsort(.(x,y)) >= last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y)))))) ;
  last(nil) >= 0 ;
  last(.(x,nil)) >= x ;
  last(.(x,.(y,z))) >= last(.(y,z)) ;
  bubble(nil) >= nil ;
  bubble(.(x,nil)) >= .(x,nil) ;
  bubble(.(x,.(y,z))) >= if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z)))) ;
  butlast(nil) >= nil ;
  butlast(.(x,nil)) >= nil ;
  butlast(.(x,.(y,z))) >= .(x,butlast(.(y,z))) ;
  Marked_bsort(.(x,y)) > Marked_bsort(butlast(bubble(.(x,y)))) ;
 }
 + Disjunctions:{ 
 } 
=== 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
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
No solution found for these parameters.(766 bt (982) [15])
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 123.700501 seconds (real time)
Cime Exit Status: 0