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

TRS termination of:
[1] a(0,b(0,x)) -> b(0,a(0,x))
[2] a(0,x) -> b(0,b(0,x))
[3] a(0,a(1,a(x,y))) -> a(1,a(0,a(x,y)))
[4] b(0,a(1,a(x,y))) -> b(1,a(0,a(x,y)))
[5] a(0,a(x,y)) -> a(1,a(1,a(x,y)))


Sub problem: 
guided: 

DP termination of:
<Marked_a(0,b(0,x)) , Marked_b(0,a(0,x))>
<Marked_a(0,b(0,x)) , Marked_a(0,x)>
<Marked_a(0,x) , Marked_b(0,b(0,x))>
<Marked_a(0,x) , Marked_b(0,x)>
<Marked_a(0,a(1,a(x,y))) , Marked_a(1,a(0,a(x,y)))>
<Marked_a(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
<Marked_b(0,a(1,a(x,y))) , Marked_b(1,a(0,a(x,y)))>
<Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
<Marked_a(0,a(x,y)) , Marked_a(1,a(1,a(x,y)))>
<Marked_a(0,a(x,y)) , Marked_a(1,a(x,y))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
      --> <Marked_a(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
  <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,x) , Marked_b(0,x)>
  <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,x) , Marked_b(0,b(0,x))>
  <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,b(0,x)) , Marked_a(0,x)>
  <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,b(0,x)) , Marked_b(0,a(0,x))>
  <Marked_a(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
  <Marked_a(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,x) , Marked_b(0,x)>
  <Marked_a(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,x) , Marked_b(0,b(0,x))>
  <Marked_a(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,b(0,x)) , Marked_a(0,x)>
  <Marked_a(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,b(0,x)) , Marked_b(0,a(0,x))>
  <Marked_a(0,x) , Marked_b(0,x)> 
     --> <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
  <Marked_a(0,x) , Marked_b(0,b(0,x))> 
     --> <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
  <Marked_a(0,b(0,x)) , Marked_a(0,x)> 
     --> <Marked_a(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
  <Marked_a(0,b(0,x)) , Marked_a(0,x)> --> <Marked_a(0,x) , Marked_b(0,x)>
  <Marked_a(0,b(0,x)) , Marked_a(0,x)> --> <Marked_a(0,x) , Marked_b(0,b(0,x))>
  <Marked_a(0,b(0,x)) , Marked_a(0,x)> --> <Marked_a(0,b(0,x)) , Marked_a(0,x)>
  <Marked_a(0,b(0,x)) , Marked_a(0,x)> 
     --> <Marked_a(0,b(0,x)) , Marked_b(0,a(0,x))>
  <Marked_a(0,b(0,x)) , Marked_b(0,a(0,x))> 
     --> <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  b(0,a(1,a(x,y))) >= b(1,a(0,a(x,y))) ;
  a(0,b(0,x)) >= b(0,a(0,x)) ;
  a(0,a(1,a(x,y))) >= a(1,a(0,a(x,y))) ;
  a(0,a(x,y)) >= a(1,a(1,a(x,y))) ;
  a(0,x) >= b(0,b(0,x)) ;
  Marked_a(0,b(0,x)) >= Marked_a(0,x) ;
  Marked_a(0,b(0,x)) >= Marked_b(0,a(0,x)) ;
  Marked_a(0,a(1,a(x,y))) >= Marked_a(0,a(x,y)) ;
  Marked_a(0,x) >= Marked_b(0,b(0,x)) ;
  Marked_a(0,x) >= Marked_b(0,x) ;
  Marked_b(0,a(1,a(x,y))) >= Marked_a(0,a(x,y)) ;
 }
 + Disjunctions:{ 
{
  Marked_a(0,b(0,x)) > Marked_a(0,x) ;
 }
{
  Marked_a(0,b(0,x)) > Marked_b(0,a(0,x)) ;
 }
{
  Marked_a(0,a(1,a(x,y))) > Marked_a(0,a(x,y)) ;
 }
{
  Marked_a(0,x) > Marked_b(0,b(0,x)) ;
 }
{
  Marked_a(0,x) > Marked_b(0,x) ;
 }
{
  Marked_b(0,a(1,a(x,y))) > Marked_a(0,a(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: b(0,a(1,a(x,y))) >= b(1,a(0,a(x,y)))
constraint: a(0,b(0,x)) >= b(0,a(0,x))
constraint: a(0,a(1,a(x,y))) >= a(1,a(0,a(x,y)))
constraint: a(0,a(x,y)) >= a(1,a(1,a(x,y)))
constraint: a(0,x) >= b(0,b(0,x))
constraint: Marked_a(0,b(0,x)) >= Marked_a(0,x)
constraint: Marked_a(0,b(0,x)) >= Marked_b(0,a(0,x))
constraint: Marked_a(0,a(1,a(x,y))) >= Marked_a(0,a(x,y))
constraint: Marked_a(0,x) >= Marked_b(0,b(0,x))
constraint: Marked_a(0,x) >= Marked_b(0,x)
constraint: Marked_b(0,a(1,a(x,y))) >= Marked_a(0,a(x,y))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
      --> <Marked_a(0,x) , Marked_b(0,b(0,x))>
  <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
     --> <Marked_a(0,b(0,x)) , Marked_b(0,a(0,x))>
  <Marked_a(0,x) , Marked_b(0,b(0,x))> 
     --> <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
  <Marked_a(0,b(0,x)) , Marked_b(0,a(0,x))> 
     --> <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  b(0,a(1,a(x,y))) >= b(1,a(0,a(x,y))) ;
  a(0,b(0,x)) >= b(0,a(0,x)) ;
  a(0,a(1,a(x,y))) >= a(1,a(0,a(x,y))) ;
  a(0,a(x,y)) >= a(1,a(1,a(x,y))) ;
  a(0,x) >= b(0,b(0,x)) ;
  Marked_a(0,b(0,x)) >= Marked_b(0,a(0,x)) ;
  Marked_a(0,x) >= Marked_b(0,b(0,x)) ;
  Marked_b(0,a(1,a(x,y))) >= Marked_a(0,a(x,y)) ;
 }
 + Disjunctions:{ 
{
  Marked_a(0,b(0,x)) > Marked_b(0,a(0,x)) ;
 }
{
  Marked_a(0,x) > Marked_b(0,b(0,x)) ;
 }
{
  Marked_b(0,a(1,a(x,y))) > Marked_a(0,a(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: b(0,a(1,a(x,y))) >= b(1,a(0,a(x,y)))
constraint: a(0,b(0,x)) >= b(0,a(0,x))
constraint: a(0,a(1,a(x,y))) >= a(1,a(0,a(x,y)))
constraint: a(0,a(x,y)) >= a(1,a(1,a(x,y)))
constraint: a(0,x) >= b(0,b(0,x))
constraint: Marked_a(0,b(0,x)) >= Marked_b(0,a(0,x))
constraint: Marked_a(0,x) >= Marked_b(0,b(0,x))
constraint: Marked_b(0,a(1,a(x,y))) >= Marked_a(0,a(x,y))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))> 
      --> <Marked_a(0,b(0,x)) , Marked_b(0,a(0,x))>
  <Marked_a(0,b(0,x)) , Marked_b(0,a(0,x))> 
     --> <Marked_b(0,a(1,a(x,y))) , Marked_a(0,a(x,y))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  b(0,a(1,a(x,y))) >= b(1,a(0,a(x,y))) ;
  a(0,b(0,x)) >= b(0,a(0,x)) ;
  a(0,a(1,a(x,y))) >= a(1,a(0,a(x,y))) ;
  a(0,a(x,y)) >= a(1,a(1,a(x,y))) ;
  a(0,x) >= b(0,b(0,x)) ;
  Marked_a(0,b(0,x)) >= Marked_b(0,a(0,x)) ;
  Marked_b(0,a(1,a(x,y))) >= Marked_a(0,a(x,y)) ;
 }
 + Disjunctions:{ 
{
  Marked_a(0,b(0,x)) > Marked_b(0,a(0,x)) ;
 }
{
  Marked_b(0,a(1,a(x,y))) > Marked_a(0,a(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 timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  b(0,a(1,a(x,y))) >= b(1,a(0,a(x,y))) ;
  a(0,b(0,x)) >= b(0,a(0,x)) ;
  a(0,a(1,a(x,y))) >= a(1,a(0,a(x,y))) ;
  a(0,a(x,y)) >= a(1,a(1,a(x,y))) ;
  a(0,x) >= b(0,b(0,x)) ;
  Marked_a(0,b(0,x)) > Marked_b(0,a(0,x)) ;
  Marked_b(0,a(1,a(x,y))) >= Marked_a(0,a(x,y)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  b(0,a(1,a(x,y))) >= b(1,a(0,a(x,y))) ;
  a(0,b(0,x)) >= b(0,a(0,x)) ;
  a(0,a(1,a(x,y))) >= a(1,a(0,a(x,y))) ;
  a(0,a(x,y)) >= a(1,a(1,a(x,y))) ;
  a(0,x) >= b(0,b(0,x)) ;
  Marked_a(0,b(0,x)) > Marked_b(0,a(0,x)) ;
  Marked_b(0,a(1,a(x,y))) >= Marked_a(0,a(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.(154 bt (41) [24])
=== 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 timeout reached
=== 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 104.069569 seconds (real time)
Cime Exit Status: 0