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

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


Sub problem: 
guided: 

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

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

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

{  <Marked_plus(s(x),y) , Marked_plus(x,y)> 
      --> <Marked_plus(s(x),y) , Marked_plus(x,y)>
  <Marked_plus(s(x),y) , Marked_plus(x,y)> 
     --> <Marked_plus(x,s(y)) , Marked_plus(x,y)>
  <Marked_plus(x,s(y)) , Marked_plus(x,y)> 
     --> <Marked_plus(s(x),y) , Marked_plus(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:
{
  help(x,y,c) >= if(lt(c,y),x,y,c) ;
  times(x,y) >= help(x,y,0) ;
  if(true,x,y,c) >= plus(x,help(x,y,s(c))) ;
  if(false,x,y,c) >= 0 ;
  lt(0,s(x)) >= true ;
  lt(s(x),0) >= false ;
  lt(s(x),s(y)) >= lt(x,y) ;
  plus(0,x) >= x ;
  plus(s(x),y) >= s(plus(x,y)) ;
  plus(x,0) >= x ;
  plus(x,s(y)) >= s(plus(x,y)) ;
  Marked_if(true,x,y,c) >= Marked_help(x,y,s(c)) ;
  Marked_help(x,y,c) >= Marked_if(lt(c,y),x,y,c) ;
 }
 + Disjunctions:{ 
{
  Marked_if(true,x,y,c) > Marked_help(x,y,s(c)) ;
 }
{
  Marked_help(x,y,c) > Marked_if(lt(c,y),x,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:
{
  help(x,y,c) >= if(lt(c,y),x,y,c) ;
  times(x,y) >= help(x,y,0) ;
  if(true,x,y,c) >= plus(x,help(x,y,s(c))) ;
  if(false,x,y,c) >= 0 ;
  lt(0,s(x)) >= true ;
  lt(s(x),0) >= false ;
  lt(s(x),s(y)) >= lt(x,y) ;
  plus(0,x) >= x ;
  plus(s(x),y) >= s(plus(x,y)) ;
  plus(x,0) >= x ;
  plus(x,s(y)) >= s(plus(x,y)) ;
  Marked_if(true,x,y,c) >= Marked_help(x,y,s(c)) ;
  Marked_help(x,y,c) > Marked_if(lt(c,y),x,y,c) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  help(x,y,c) >= if(lt(c,y),x,y,c) ;
  times(x,y) >= help(x,y,0) ;
  if(true,x,y,c) >= plus(x,help(x,y,s(c))) ;
  if(false,x,y,c) >= 0 ;
  lt(0,s(x)) >= true ;
  lt(s(x),0) >= false ;
  lt(s(x),s(y)) >= lt(x,y) ;
  plus(0,x) >= x ;
  plus(s(x),y) >= s(plus(x,y)) ;
  plus(x,0) >= x ;
  plus(x,s(y)) >= s(plus(x,y)) ;
  Marked_if(true,x,y,c) >= Marked_help(x,y,s(c)) ;
  Marked_help(x,y,c) > Marked_if(lt(c,y),x,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.(13873 bt (13735) [1412])
=== 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 1.537330 seconds (real time)
Cime Exit Status: 0