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

TRS termination of:
[1] p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3)))


Sub problem: 
guided: 

DP termination of:
<Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,p(a(a(x0)),p(b(x1),x3)))>
<Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(a(a(x0)),p(b(x1),x3))>
<Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(b(x1),x3)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(a(a(x0)),p(b(x1),x3))> 
      --> <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(a(a(x0)),
                                                   p(b(x1),x3))>
  <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(a(a(x0)),p(b(x1),x3))> 
     --> <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,
                                                  p(a(a(x0)),p(b(x1),x3)))>
  <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,p(a(a(x0)),p(b(x1),x3)))> 
     --> <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(a(a(x0)),p(b(x1),x3))>
  <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,p(a(a(x0)),p(b(x1),x3)))> 
     --> <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,
                                                  p(a(a(x0)),p(b(x1),x3)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  p(a(x0),p(b(x1),p(a(x2),x3))) >= p(x2,p(a(a(x0)),p(b(x1),x3))) ;
  Marked_p(a(x0),p(b(x1),p(a(x2),x3))) >= Marked_p(a(a(x0)),p(b(x1),x3)) ;
  Marked_p(a(x0),p(b(x1),p(a(x2),x3))) >= Marked_p(x2,p(a(a(x0)),p(b(x1),x3))) ;
 }
 + Disjunctions:{ 
{
  Marked_p(a(x0),p(b(x1),p(a(x2),x3))) > Marked_p(a(a(x0)),p(b(x1),x3)) ;
 }
{
  Marked_p(a(x0),p(b(x1),p(a(x2),x3))) > Marked_p(x2,p(a(a(x0)),p(b(x1),x3))) ;
 }
 } 
=== 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: p(a(x0),p(b(x1),p(a(x2),x3))) >= p(x2,p(a(a(x0)),p(b(x1),x3)))
constraint: Marked_p(a(x0),p(b(x1),p(a(x2),x3))) >= Marked_p(a(a(x0)),
                                                     p(b(x1),x3))
constraint: Marked_p(a(x0),p(b(x1),p(a(x2),x3))) >= Marked_p(x2,
                                                     p(a(a(x0)),p(b(x1),x3)))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,p(a(a(x0)),p(b(x1),x3)))> 
      --> <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,
                                                   p(a(a(x0)),p(b(x1),x3)))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  p(a(x0),p(b(x1),p(a(x2),x3))) >= p(x2,p(a(a(x0)),p(b(x1),x3))) ;
  Marked_p(a(x0),p(b(x1),p(a(x2),x3))) >= Marked_p(x2,p(a(a(x0)),p(b(x1),x3))) ;
 }
 + Disjunctions:{ 
{
  Marked_p(a(x0),p(b(x1),p(a(x2),x3))) > Marked_p(x2,p(a(a(x0)),p(b(x1),x3))) ;
 }
 } 
=== 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 : 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: p(a(x0),p(b(x1),p(a(x2),x3))) >= p(x2,p(a(a(x0)),p(b(x1),x3)))
constraint: Marked_p(a(x0),p(b(x1),p(a(x2),x3))) >= Marked_p(x2,
                                                     p(a(a(x0)),p(b(x1),x3)))
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,
                                              p(a(a(x0)),p(b(x1),x3)))>
<Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(a(a(x0)),p(b(x1),x3))>
<Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(b(x1),x3)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,
                                              p(a(a(x0)),p(b(x1),x3)))>
<Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(a(a(x0)),p(b(x1),x3))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ p ] (X0,X1) = 2*X1 + 2; 
 [ b ] (X0) = 0; 
 [ a ] (X0) = 0; 
 [ Marked_p ] (X0,X1) = 2*X1; 
 removing <Marked_p(a(x0),p(b(x1),p(a(x2),x3))),Marked_p(a(a(x0)),p(b(x1),x3))>
 [ {
      
     DP termination of:
     <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,
                                              p(a(a(x0)),p(b(x1),x3)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_p(a(x0),p(b(x1),p(a(x2),x3))) , Marked_p(x2,
                                              p(a(a(x0)),p(b(x1),x3)))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ p ] (X0,X1) = 2*X0 + 2*X1 + 1*X1*X0 + 0; 
 [ b ] (X0) = 0; 
 [ a ] (X0) = 2 + 2*X0 + 0; 
 [ Marked_p ] (X0,X1) = 2*X1 + 1*X1*X0 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.938598 seconds (real time)
Cime Exit Status: 0