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

TRS termination of:
[1] a(a(x)) -> b(b(x))
[2] b(b(a(x))) -> a(b(b(x)))


Sub problem: 
guided: 

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

{  <Marked_b(b(a(x))) , Marked_b(x)> --> <Marked_b(b(a(x))) , Marked_b(x)>
  <Marked_b(b(a(x))) , Marked_b(x)> --> <Marked_b(b(a(x))) , Marked_b(b(x))>
  <Marked_b(b(a(x))) , Marked_b(x)> --> <Marked_b(b(a(x))) , Marked_a(b(b(x)))>
  <Marked_b(b(a(x))) , Marked_b(b(x))> --> <Marked_b(b(a(x))) , Marked_b(x)>
  <Marked_b(b(a(x))) , Marked_b(b(x))> --> <Marked_b(b(a(x))) , Marked_b(b(x))>
  <Marked_b(b(a(x))) , Marked_b(b(x))> 
     --> <Marked_b(b(a(x))) , Marked_a(b(b(x)))>
  <Marked_b(b(a(x))) , Marked_a(b(b(x)))> --> <Marked_a(a(x)) , Marked_b(x)>
  <Marked_b(b(a(x))) , Marked_a(b(b(x)))> --> <Marked_a(a(x)) , Marked_b(b(x))>
  <Marked_a(a(x)) , Marked_b(x)> --> <Marked_b(b(a(x))) , Marked_b(x)>
  <Marked_a(a(x)) , Marked_b(x)> --> <Marked_b(b(a(x))) , Marked_b(b(x))>
  <Marked_a(a(x)) , Marked_b(x)> --> <Marked_b(b(a(x))) , Marked_a(b(b(x)))>
  <Marked_a(a(x)) , Marked_b(b(x))> --> <Marked_b(b(a(x))) , Marked_b(x)>
  <Marked_a(a(x)) , Marked_b(b(x))> --> <Marked_b(b(a(x))) , Marked_b(b(x))>
  <Marked_a(a(x)) , Marked_b(b(x))> --> <Marked_b(b(a(x))) , Marked_a(b(b(x)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  b(b(a(x))) >= a(b(b(x))) ;
  a(a(x)) >= b(b(x)) ;
  Marked_b(b(a(x))) >= Marked_b(b(x)) ;
  Marked_b(b(a(x))) >= Marked_b(x) ;
  Marked_b(b(a(x))) >= Marked_a(b(b(x))) ;
  Marked_a(a(x)) >= Marked_b(b(x)) ;
  Marked_a(a(x)) >= Marked_b(x) ;
 }
 + Disjunctions:{ 
{
  Marked_b(b(a(x))) > Marked_b(b(x)) ;
 }
{
  Marked_b(b(a(x))) > Marked_b(x) ;
 }
{
  Marked_b(b(a(x))) > Marked_a(b(b(x))) ;
 }
{
  Marked_a(a(x)) > Marked_b(b(x)) ;
 }
{
  Marked_a(a(x)) > Marked_b(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: b(b(a(x))) >= a(b(b(x)))
constraint: a(a(x)) >= b(b(x))
constraint: Marked_b(b(a(x))) >= Marked_b(b(x))
constraint: Marked_b(b(a(x))) >= Marked_b(x)
constraint: Marked_b(b(a(x))) >= Marked_a(b(b(x)))
constraint: Marked_a(a(x)) >= Marked_b(b(x))
constraint: Marked_a(a(x)) >= Marked_b(x)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a(a(x)) -> b(b(x))
[2] b(b(a(x))) -> a(b(b(x)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a(a(x)) , Marked_b(b(x))>
<Marked_a(a(x)) , Marked_b(x)>
<Marked_b(b(a(x))) , Marked_a(b(b(x)))>
<Marked_b(b(a(x))) , Marked_b(b(x))>
<Marked_b(b(a(x))) , Marked_b(x)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a(a(x)) , Marked_b(b(x))>
<Marked_a(a(x)) , Marked_b(x)>
<Marked_b(b(a(x))) , Marked_a(b(b(x)))>
<Marked_b(b(a(x))) , Marked_b(b(x))>
<Marked_b(b(a(x))) , Marked_b(x)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ b ] (X0) = 1*X0 + 0; 
 [ Marked_b ] (X0) = 2 + 1*X0 + 0; 
 [ a ] (X0) = 2 + 3*X0 + 0; 
 [ Marked_a ] (X0) = 2 + 1*X0 + 0; 
 ]} 
 ]} 
 ]} 

Cime worked for 0.030887 seconds (real time)
Cime Exit Status: 0