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

TRS termination of:
[1] lt(x,0) -> false
[2] lt(0,s(y)) -> true
[3] lt(s(x),s(y)) -> lt(x,y)
[4] plus(x,0) -> x
[5] plus(x,s(y)) -> s(plus(x,y))
[6] quot(x,s(y)) -> help(x,s(y),0)
[7] help(x,s(y),c) -> if(lt(c,x),x,s(y),c)
[8] if(true,x,s(y),c) -> s(help(x,s(y),plus(c,s(y))))
[9] if(false,x,s(y),c) -> 0


Sub problem: 
guided: 

DP termination of:
<Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
<Marked_plus(x,s(y)) , Marked_plus(x,y)>
<Marked_quot(x,s(y)) , Marked_help(x,s(y),0)>
<Marked_help(x,s(y),c) , Marked_if(lt(c,x),x,s(y),c)>
<Marked_help(x,s(y),c) , Marked_lt(c,x)>
<Marked_if(true,x,s(y),c) , Marked_help(x,s(y),plus(c,s(y)))>
<Marked_if(true,x,s(y),c) , Marked_plus(c,s(y))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_if(true,x,s(y),c) , Marked_help(x,s(y),plus(c,s(y)))> 
      --> <Marked_help(x,s(y),c) , Marked_if(lt(c,x),x,s(y),c)>
  <Marked_help(x,s(y),c) , Marked_if(lt(c,x),x,s(y),c)> 
     --> <Marked_if(true,x,s(y),c) , Marked_help(x,s(y),plus(c,s(y)))>
}

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

{  <Marked_plus(x,s(y)) , Marked_plus(x,y)> 
      --> <Marked_plus(x,s(y)) , Marked_plus(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  plus(x,0) >= x ;
  plus(x,s(y)) >= s(plus(x,y)) ;
  help(x,s(y),c) >= if(lt(c,x),x,s(y),c) ;
  quot(x,s(y)) >= help(x,s(y),0) ;
  if(false,x,s(y),c) >= 0 ;
  if(true,x,s(y),c) >= s(help(x,s(y),plus(c,s(y)))) ;
  Marked_if(true,x,s(y),c) >= Marked_help(x,s(y),plus(c,s(y))) ;
  Marked_help(x,s(y),c) >= Marked_if(lt(c,x),x,s(y),c) ;
 }
 + Disjunctions:{ 
{
  Marked_if(true,x,s(y),c) > Marked_help(x,s(y),plus(c,s(y))) ;
 }
{
  Marked_help(x,s(y),c) > Marked_if(lt(c,x),x,s(y),c) ;
 }
 } 
=== 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 solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  plus(x,0) >= x ;
  plus(x,s(y)) >= s(plus(x,y)) ;
  help(x,s(y),c) >= if(lt(c,x),x,s(y),c) ;
  quot(x,s(y)) >= help(x,s(y),0) ;
  if(false,x,s(y),c) >= 0 ;
  if(true,x,s(y),c) >= s(help(x,s(y),plus(c,s(y)))) ;
  Marked_if(true,x,s(y),c) >= Marked_help(x,s(y),plus(c,s(y))) ;
  Marked_help(x,s(y),c) > Marked_if(lt(c,x),x,s(y),c) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  plus(x,0) >= x ;
  plus(x,s(y)) >= s(plus(x,y)) ;
  help(x,s(y),c) >= if(lt(c,x),x,s(y),c) ;
  quot(x,s(y)) >= help(x,s(y),0) ;
  if(false,x,s(y),c) >= 0 ;
  if(true,x,s(y),c) >= s(help(x,s(y),plus(c,s(y)))) ;
  Marked_if(true,x,s(y),c) >= Marked_help(x,s(y),plus(c,s(y))) ;
  Marked_help(x,s(y),c) > Marked_if(lt(c,x),x,s(y),c) ;
 }
 + 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.(19951 bt (19511) [2040])
=== 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 solver returned
=== STOPING TIMER real ===
=== 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 4.460869 seconds (real time)
Cime Exit Status: 0