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

TRS termination of:
[1] numbers -> d(0)
[2] d(x) -> if(le(x,nr),x)
[3] if(true,x) -> cons(x,d(s(x)))
[4] if(false,x) -> nil
[5] le(0,y) -> true
[6] le(s(x),0) -> false
[7] le(s(x),s(y)) -> le(x,y)
[8] nr -> ack(s(s(s(s(s(s(0)))))),0)
[9] ack(0,x) -> s(x)
[10] ack(s(x),0) -> ack(x,s(0))
[11] ack(s(x),s(y)) -> ack(x,ack(s(x),y))


Sub problem: 
guided: 

DP termination of:
<Marked_numbers , Marked_d(0)>
<Marked_d(x) , Marked_if(le(x,nr),x)>
<Marked_d(x) , Marked_le(x,nr)>
<Marked_d(x) , Marked_nr>
<Marked_if(true,x) , Marked_d(s(x))>
<Marked_le(s(x),s(y)) , Marked_le(x,y)>
<Marked_nr , Marked_ack(s(s(s(s(s(s(0)))))),0)>
<Marked_ack(s(x),0) , Marked_ack(x,s(0))>
<Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
<Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_if(true,x) , Marked_d(s(x))> 
      --> <Marked_d(x) , Marked_if(le(x,nr),x)>
  <Marked_d(x) , Marked_if(le(x,nr),x)> 
     --> <Marked_if(true,x) , Marked_d(s(x))>
}

{  <Marked_le(s(x),s(y)) , Marked_le(x,y)> 
      --> <Marked_le(s(x),s(y)) , Marked_le(x,y)>
}

{  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
      --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
  <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)> 
     --> <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
  <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))> 
     --> <Marked_ack(s(x),0) , Marked_ack(x,s(0))>
  <Marked_ack(s(x),0) , Marked_ack(x,s(0))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(s(x),y)>
  <Marked_ack(s(x),0) , Marked_ack(x,s(0))> 
     --> <Marked_ack(s(x),s(y)) , Marked_ack(x,ack(s(x),y))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  d(x) >= if(le(x,nr),x) ;
  numbers >= d(0) ;
  if(true,x) >= cons(x,d(s(x))) ;
  if(false,x) >= nil ;
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  nr >= ack(s(s(s(s(s(s(0)))))),0) ;
  ack(0,x) >= s(x) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ;
  Marked_if(true,x) >= Marked_d(s(x)) ;
  Marked_d(x) >= Marked_if(le(x,nr),x) ;
 }
 + Disjunctions:{ 
{
  Marked_if(true,x) > Marked_d(s(x)) ;
 }
{
  Marked_d(x) > Marked_if(le(x,nr),x) ;
 }
 } 
=== 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 : 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:
{
  d(x) >= if(le(x,nr),x) ;
  numbers >= d(0) ;
  if(true,x) >= cons(x,d(s(x))) ;
  if(false,x) >= nil ;
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  nr >= ack(s(s(s(s(s(s(0)))))),0) ;
  ack(0,x) >= s(x) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ;
  Marked_if(true,x) >= Marked_d(s(x)) ;
  Marked_d(x) > Marked_if(le(x,nr),x) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  d(x) >= if(le(x,nr),x) ;
  numbers >= d(0) ;
  if(true,x) >= cons(x,d(s(x))) ;
  if(false,x) >= nil ;
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  nr >= ack(s(s(s(s(s(s(0)))))),0) ;
  ack(0,x) >= s(x) ;
  ack(s(x),0) >= ack(x,s(0)) ;
  ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ;
  Marked_if(true,x) >= Marked_d(s(x)) ;
  Marked_d(x) > Marked_if(le(x,nr),x) ;
 }
 + 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.(5613 bt (5261) [640])
=== 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 139.784443 seconds (real time)
Cime Exit Status: 0