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

TRS termination of:
[1] division(x,y) -> div(x,y,0)
[2] div(x,y,z) -> if(lt(x,y),x,y,inc(z))
[3] if(true,x,y,z) -> z
[4] if(false,x,s(y),z) -> div(minus(x,s(y)),s(y),z)
[5] minus(x,0) -> x
[6] minus(s(x),s(y)) -> minus(x,y)
[7] lt(x,0) -> false
[8] lt(0,s(y)) -> true
[9] lt(s(x),s(y)) -> lt(x,y)
[10] inc(0) -> s(0)
[11] inc(s(x)) -> s(inc(x))


Sub problem: 
guided: 

DP termination of:
<Marked_division(x,y) , Marked_div(x,y,0)>
<Marked_div(x,y,z) , Marked_if(lt(x,y),x,y,inc(z))>
<Marked_div(x,y,z) , Marked_lt(x,y)>
<Marked_div(x,y,z) , Marked_inc(z)>
<Marked_if(false,x,s(y),z) , Marked_div(minus(x,s(y)),s(y),z)>
<Marked_if(false,x,s(y),z) , Marked_minus(x,s(y))>
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_lt(s(x),s(y)) , Marked_lt(x,y)>
<Marked_inc(s(x)) , Marked_inc(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_if(false,x,s(y),z) , Marked_div(minus(x,s(y)),s(y),z)> 
      --> <Marked_div(x,y,z) , Marked_if(lt(x,y),x,y,inc(z))>
  <Marked_div(x,y,z) , Marked_if(lt(x,y),x,y,inc(z))> 
     --> <Marked_if(false,x,s(y),z) , Marked_div(minus(x,s(y)),s(y),z)>
}

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

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

{  <Marked_inc(s(x)) , Marked_inc(x)> --> <Marked_inc(s(x)) , Marked_inc(x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  div(x,y,z) >= if(lt(x,y),x,y,inc(z)) ;
  division(x,y) >= div(x,y,0) ;
  if(true,x,y,z) >= z ;
  if(false,x,s(y),z) >= div(minus(x,s(y)),s(y),z) ;
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  inc(0) >= s(0) ;
  inc(s(x)) >= s(inc(x)) ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  Marked_if(false,x,s(y),z) >= Marked_div(minus(x,s(y)),s(y),z) ;
  Marked_div(x,y,z) >= Marked_if(lt(x,y),x,y,inc(z)) ;
 }
 + Disjunctions:{ 
{
  Marked_if(false,x,s(y),z) > Marked_div(minus(x,s(y)),s(y),z) ;
 }
{
  Marked_div(x,y,z) > Marked_if(lt(x,y),x,y,inc(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
=== 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:
{
  div(x,y,z) >= if(lt(x,y),x,y,inc(z)) ;
  division(x,y) >= div(x,y,0) ;
  if(true,x,y,z) >= z ;
  if(false,x,s(y),z) >= div(minus(x,s(y)),s(y),z) ;
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  inc(0) >= s(0) ;
  inc(s(x)) >= s(inc(x)) ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  Marked_if(false,x,s(y),z) >= Marked_div(minus(x,s(y)),s(y),z) ;
  Marked_div(x,y,z) > Marked_if(lt(x,y),x,y,inc(z)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  div(x,y,z) >= if(lt(x,y),x,y,inc(z)) ;
  division(x,y) >= div(x,y,0) ;
  if(true,x,y,z) >= z ;
  if(false,x,s(y),z) >= div(minus(x,s(y)),s(y),z) ;
  lt(0,s(y)) >= true ;
  lt(s(x),s(y)) >= lt(x,y) ;
  lt(x,0) >= false ;
  inc(0) >= s(0) ;
  inc(s(x)) >= s(inc(x)) ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  Marked_if(false,x,s(y),z) >= Marked_div(minus(x,s(y)),s(y),z) ;
  Marked_div(x,y,z) > Marked_if(lt(x,y),x,y,inc(z)) ;
 }
 + 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.(41512 bt (43641) [2436])
=== 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 4.499337 seconds (real time)
Cime Exit Status: 0