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

TRS termination of:
[1] cond1(true,x) -> cond2(even(x),x)
[2] cond2(true,x) -> cond1(neq(x,0),div2(x))
[3] cond2(false,x) -> cond1(neq(x,0),p(x))
[4] neq(0,0) -> false
[5] neq(0,s(x)) -> true
[6] neq(s(x),0) -> true
[7] neq(s(x),s(y)) -> neq(x,y)
[8] even(0) -> true
[9] even(s(0)) -> false
[10] even(s(s(x))) -> even(x)
[11] div2(0) -> 0
[12] div2(s(0)) -> 0
[13] div2(s(s(x))) -> s(div2(x))
[14] p(0) -> 0
[15] p(s(x)) -> x


Sub problem: 
guided: 

DP termination of:
<Marked_cond1(true,x) , Marked_cond2(even(x),x)>
<Marked_cond1(true,x) , Marked_even(x)>
<Marked_cond2(true,x) , Marked_cond1(neq(x,0),div2(x))>
<Marked_cond2(true,x) , Marked_neq(x,0)>
<Marked_cond2(true,x) , Marked_div2(x)>
<Marked_cond2(false,x) , Marked_cond1(neq(x,0),p(x))>
<Marked_cond2(false,x) , Marked_neq(x,0)>
<Marked_cond2(false,x) , Marked_p(x)>
<Marked_neq(s(x),s(y)) , Marked_neq(x,y)>
<Marked_even(s(s(x))) , Marked_even(x)>
<Marked_div2(s(s(x))) , Marked_div2(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_cond2(false,x) , Marked_cond1(neq(x,0),p(x))> 
      --> <Marked_cond1(true,x) , Marked_cond2(even(x),x)>
  <Marked_cond2(true,x) , Marked_cond1(neq(x,0),div2(x))> 
     --> <Marked_cond1(true,x) , Marked_cond2(even(x),x)>
  <Marked_cond1(true,x) , Marked_cond2(even(x),x)> 
     --> <Marked_cond2(false,x) , Marked_cond1(neq(x,0),p(x))>
  <Marked_cond1(true,x) , Marked_cond2(even(x),x)> 
     --> <Marked_cond2(true,x) , Marked_cond1(neq(x,0),div2(x))>
}

{  <Marked_even(s(s(x))) , Marked_even(x)> 
      --> <Marked_even(s(s(x))) , Marked_even(x)>
}

{  <Marked_div2(s(s(x))) , Marked_div2(x)> 
      --> <Marked_div2(s(s(x))) , Marked_div2(x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cond2(true,x) >= cond1(neq(x,0),div2(x)) ;
  cond2(false,x) >= cond1(neq(x,0),p(x)) ;
  even(0) >= true ;
  even(s(0)) >= false ;
  even(s(s(x))) >= even(x) ;
  cond1(true,x) >= cond2(even(x),x) ;
  neq(0,0) >= false ;
  neq(0,s(x)) >= true ;
  neq(s(x),0) >= true ;
  neq(s(x),s(y)) >= neq(x,y) ;
  div2(0) >= 0 ;
  div2(s(0)) >= 0 ;
  div2(s(s(x))) >= s(div2(x)) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  Marked_cond2(true,x) >= Marked_cond1(neq(x,0),div2(x)) ;
  Marked_cond2(false,x) >= Marked_cond1(neq(x,0),p(x)) ;
  Marked_cond1(true,x) >= Marked_cond2(even(x),x) ;
 }
 + Disjunctions:{ 
{
  Marked_cond2(true,x) > Marked_cond1(neq(x,0),div2(x)) ;
 }
{
  Marked_cond2(false,x) > Marked_cond1(neq(x,0),p(x)) ;
 }
{
  Marked_cond1(true,x) > Marked_cond2(even(x),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 : 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:
{
  cond2(true,x) >= cond1(neq(x,0),div2(x)) ;
  cond2(false,x) >= cond1(neq(x,0),p(x)) ;
  even(0) >= true ;
  even(s(0)) >= false ;
  even(s(s(x))) >= even(x) ;
  cond1(true,x) >= cond2(even(x),x) ;
  neq(0,0) >= false ;
  neq(0,s(x)) >= true ;
  neq(s(x),0) >= true ;
  neq(s(x),s(y)) >= neq(x,y) ;
  div2(0) >= 0 ;
  div2(s(0)) >= 0 ;
  div2(s(s(x))) >= s(div2(x)) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  Marked_cond2(true,x) > Marked_cond1(neq(x,0),div2(x)) ;
  Marked_cond2(false,x) >= Marked_cond1(neq(x,0),p(x)) ;
  Marked_cond1(true,x) > Marked_cond2(even(x),x) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  cond2(true,x) >= cond1(neq(x,0),div2(x)) ;
  cond2(false,x) >= cond1(neq(x,0),p(x)) ;
  even(0) >= true ;
  even(s(0)) >= false ;
  even(s(s(x))) >= even(x) ;
  cond1(true,x) >= cond2(even(x),x) ;
  neq(0,0) >= false ;
  neq(0,s(x)) >= true ;
  neq(s(x),0) >= true ;
  neq(s(x),s(y)) >= neq(x,y) ;
  div2(0) >= 0 ;
  div2(s(0)) >= 0 ;
  div2(s(s(x))) >= s(div2(x)) ;
  p(0) >= 0 ;
  p(s(x)) >= x ;
  Marked_cond2(true,x) > Marked_cond1(neq(x,0),div2(x)) ;
  Marked_cond2(false,x) >= Marked_cond1(neq(x,0),p(x)) ;
  Marked_cond1(true,x) > Marked_cond2(even(x),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.(14186 bt (10087) [1778])
=== 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 6.424138 seconds (real time)
Cime Exit Status: 0