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

TRS termination of:
[1] ge(x,0) -> true
[2] ge(0,s(y)) -> false
[3] ge(s(x),s(y)) -> ge(x,y)
[4] minus(x,0) -> x
[5] minus(0,y) -> 0
[6] minus(s(x),s(y)) -> minus(x,y)
[7] id_inc(x) -> x
[8] id_inc(x) -> s(x)
[9] div(x,y) -> if(ge(y,s(0)),ge(x,y),x,y)
[10] if(false,b,x,y) -> div_by_zero
[11] if(true,false,x,y) -> 0
[12] if(true,true,x,y) -> id_inc(div(minus(x,y),y))


Sub problem: 
guided: 

DP termination of:
<Marked_ge(s(x),s(y)) , Marked_ge(x,y)>
<Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
<Marked_div(x,y) , Marked_if(ge(y,s(0)),ge(x,y),x,y)>
<Marked_div(x,y) , Marked_ge(y,s(0))>
<Marked_div(x,y) , Marked_ge(x,y)>
<Marked_if(true,true,x,y) , Marked_id_inc(div(minus(x,y),y))>
<Marked_if(true,true,x,y) , Marked_div(minus(x,y),y)>
<Marked_if(true,true,x,y) , Marked_minus(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_if(true,true,x,y) , Marked_div(minus(x,y),y)> 
      --> <Marked_div(x,y) , Marked_if(ge(y,s(0)),ge(x,y),x,y)>
  <Marked_div(x,y) , Marked_if(ge(y,s(0)),ge(x,y),x,y)> 
     --> <Marked_if(true,true,x,y) , Marked_div(minus(x,y),y)>
}

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

{  <Marked_minus(s(x),s(y)) , Marked_minus(x,y)> 
      --> <Marked_minus(s(x),s(y)) , Marked_minus(x,y)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  ge(0,s(y)) >= false ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(x,0) >= true ;
  minus(0,y) >= 0 ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  id_inc(x) >= s(x) ;
  id_inc(x) >= x ;
  if(true,true,x,y) >= id_inc(div(minus(x,y),y)) ;
  if(true,false,x,y) >= 0 ;
  if(false,b,x,y) >= div_by_zero ;
  div(x,y) >= if(ge(y,s(0)),ge(x,y),x,y) ;
  Marked_if(true,true,x,y) >= Marked_div(minus(x,y),y) ;
  Marked_div(x,y) >= Marked_if(ge(y,s(0)),ge(x,y),x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_if(true,true,x,y) > Marked_div(minus(x,y),y) ;
 }
{
  Marked_div(x,y) > Marked_if(ge(y,s(0)),ge(x,y),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 : 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:
{
  ge(0,s(y)) >= false ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(x,0) >= true ;
  minus(0,y) >= 0 ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  id_inc(x) >= s(x) ;
  id_inc(x) >= x ;
  if(true,true,x,y) >= id_inc(div(minus(x,y),y)) ;
  if(true,false,x,y) >= 0 ;
  if(false,b,x,y) >= div_by_zero ;
  div(x,y) >= if(ge(y,s(0)),ge(x,y),x,y) ;
  Marked_if(true,true,x,y) >= Marked_div(minus(x,y),y) ;
  Marked_div(x,y) > Marked_if(ge(y,s(0)),ge(x,y),x,y) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  ge(0,s(y)) >= false ;
  ge(s(x),s(y)) >= ge(x,y) ;
  ge(x,0) >= true ;
  minus(0,y) >= 0 ;
  minus(s(x),s(y)) >= minus(x,y) ;
  minus(x,0) >= x ;
  id_inc(x) >= s(x) ;
  id_inc(x) >= x ;
  if(true,true,x,y) >= id_inc(div(minus(x,y),y)) ;
  if(true,false,x,y) >= 0 ;
  if(false,b,x,y) >= div_by_zero ;
  div(x,y) >= if(ge(y,s(0)),ge(x,y),x,y) ;
  Marked_if(true,true,x,y) >= Marked_div(minus(x,y),y) ;
  Marked_div(x,y) > Marked_if(ge(y,s(0)),ge(x,y),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.(7788 bt (6953) [412])
=== 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 4.331127 seconds (real time)
Cime Exit Status: 0