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

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


Sub problem: 
guided: 

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

{  <Marked_f(b(x),b(y)) , Marked_f(x,y)> 
      --> <Marked_f(b(x),b(y)) , Marked_f(x,y)>
  <Marked_f(b(x),b(y)) , Marked_f(x,y)> 
     --> <Marked_f(a(x),a(y)) , Marked_f(x,y)>
  <Marked_f(b(x),b(y)) , Marked_f(x,y)> 
     --> <Marked_f(a(x),a(y)) , Marked_a(f(x,y))>
  <Marked_f(a(x),a(y)) , Marked_f(x,y)> 
     --> <Marked_f(b(x),b(y)) , Marked_f(x,y)>
  <Marked_f(a(x),a(y)) , Marked_f(x,y)> 
     --> <Marked_f(a(x),a(y)) , Marked_f(x,y)>
  <Marked_f(a(x),a(y)) , Marked_f(x,y)> 
     --> <Marked_f(a(x),a(y)) , Marked_a(f(x,y))>
  <Marked_f(a(x),a(y)) , Marked_a(f(x,y))> 
     --> <Marked_a(a(f(x,y))) , Marked_a(y)>
  <Marked_f(a(x),a(y)) , Marked_a(f(x,y))> 
     --> <Marked_a(a(f(x,y))) , Marked_a(x)>
  <Marked_f(a(x),a(y)) , Marked_a(f(x,y))> 
     --> <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))>
  <Marked_a(a(f(x,y))) , Marked_a(y)> --> <Marked_a(a(f(x,y))) , Marked_a(y)>
  <Marked_a(a(f(x,y))) , Marked_a(y)> --> <Marked_a(a(f(x,y))) , Marked_a(x)>
  <Marked_a(a(f(x,y))) , Marked_a(y)> 
     --> <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))>
  <Marked_a(a(f(x,y))) , Marked_a(x)> --> <Marked_a(a(f(x,y))) , Marked_a(y)>
  <Marked_a(a(f(x,y))) , Marked_a(x)> --> <Marked_a(a(f(x,y))) , Marked_a(x)>
  <Marked_a(a(f(x,y))) , Marked_a(x)> 
     --> <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))>
  <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))> 
     --> <Marked_f(b(x),b(y)) , Marked_f(x,y)>
  <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))> 
     --> <Marked_f(a(x),a(y)) , Marked_f(x,y)>
  <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))> 
     --> <Marked_f(a(x),a(y)) , Marked_a(f(x,y))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(a(x),a(y)) >= a(f(x,y)) ;
  f(b(x),b(y)) >= b(f(x,y)) ;
  a(a(f(x,y))) >= f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) ;
  Marked_f(a(x),a(y)) >= Marked_f(x,y) ;
  Marked_f(a(x),a(y)) >= Marked_a(f(x,y)) ;
  Marked_f(b(x),b(y)) >= Marked_f(x,y) ;
  Marked_a(a(f(x,y))) >= Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) ;
  Marked_a(a(f(x,y))) >= Marked_a(x) ;
  Marked_a(a(f(x,y))) >= Marked_a(y) ;
 }
 + Disjunctions:{ 
{
  Marked_f(a(x),a(y)) > Marked_f(x,y) ;
 }
{
  Marked_f(a(x),a(y)) > Marked_a(f(x,y)) ;
 }
{
  Marked_f(b(x),b(y)) > Marked_f(x,y) ;
 }
{
  Marked_a(a(f(x,y))) > Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y)))))) ;
 }
{
  Marked_a(a(f(x,y))) > Marked_a(x) ;
 }
{
  Marked_a(a(f(x,y))) > Marked_a(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: f(a(x),a(y)) >= a(f(x,y))
constraint: f(b(x),b(y)) >= b(f(x,y))
constraint: a(a(f(x,y))) >= f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
constraint: Marked_f(a(x),a(y)) >= Marked_f(x,y)
constraint: Marked_f(a(x),a(y)) >= Marked_a(f(x,y))
constraint: Marked_f(b(x),b(y)) >= Marked_f(x,y)
constraint: Marked_a(a(f(x,y))) >= Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
constraint: Marked_a(a(f(x,y))) >= Marked_a(x)
constraint: Marked_a(a(f(x,y))) >= Marked_a(y)
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

{  <Marked_f(b(x),b(y)) , Marked_f(x,y)> 
      --> <Marked_f(b(x),b(y)) , Marked_f(x,y)>
  <Marked_f(b(x),b(y)) , Marked_f(x,y)> 
     --> <Marked_f(a(x),a(y)) , Marked_f(x,y)>
  <Marked_f(a(x),a(y)) , Marked_f(x,y)> 
     --> <Marked_f(b(x),b(y)) , Marked_f(x,y)>
  <Marked_f(a(x),a(y)) , Marked_f(x,y)> 
     --> <Marked_f(a(x),a(y)) , Marked_f(x,y)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_f -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a(a(f(x,y))) -> f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))
[2] f(a(x),a(y)) -> a(f(x,y))
[3] f(b(x),b(y)) -> b(f(x,y))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))>
<Marked_a(a(f(x,y))) , Marked_a(b(a(b(a(x)))))>
<Marked_a(a(f(x,y))) , Marked_a(b(a(x)))>
<Marked_a(a(f(x,y))) , Marked_a(x)>
<Marked_a(a(f(x,y))) , Marked_a(b(a(b(a(y)))))>
<Marked_a(a(f(x,y))) , Marked_a(b(a(y)))>
<Marked_a(a(f(x,y))) , Marked_a(y)>
<Marked_f(a(x),a(y)) , Marked_a(f(x,y))>
<Marked_f(a(x),a(y)) , Marked_f(x,y)>
<Marked_f(b(x),b(y)) , Marked_f(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))>
<Marked_a(a(f(x,y))) , Marked_a(x)>
<Marked_a(a(f(x,y))) , Marked_a(y)>
<Marked_f(a(x),a(y)) , Marked_a(f(x,y))>
<Marked_f(a(x),a(y)) , Marked_f(x,y)>
<Marked_f(b(x),b(y)) , Marked_f(x,y)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ f ] (X0,X1) = 1*X1 + 1*X0 + 1; 
 [ Marked_a ] (X0) = 2*X0; 
 [ b ] (X0) = 1*X0; 
 [ a ] (X0) = 1*X0; 
 [ Marked_f ] (X0,X1) = 2*X1 + 2*X0 + 2; 
 removing <Marked_a(a(f(x,y))),Marked_a(x)><Marked_a(a(f(x,y))),Marked_a(y)>
 [ {
      
     DP termination of:
     <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))>
<Marked_f(a(x),a(y)) , Marked_a(f(x,y))>
<Marked_f(a(x),a(y)) , Marked_f(x,y)>
<Marked_f(b(x),b(y)) , Marked_f(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a(a(f(x,y))) , Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))>
<Marked_f(a(x),a(y)) , Marked_a(f(x,y))>
<Marked_f(a(x),a(y)) , Marked_f(x,y)>
<Marked_f(b(x),b(y)) , Marked_f(x,y)>
 ,
 CRITERION: CG using Matrix polynomial interpretation (strict sub matrices size: 1x1) = 
 [ f ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 1 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 1 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_a ] (X0) = [ [ 1 , 0 , 1 ] [ 0 , 0 , 0 ] [ 1 , 1 , 0 ] ]*X0 + 
[ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 [ b ] (X0) = [ [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ a ] (X0) = [ [ 0 , 0 , 0 ] [ 1 , 1 , 0 ] [ 1 , 0 , 1 ] ]*X0 + [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; 
 [ Marked_f ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + 
[ [ 0 , 1 , 0 ] [ 0 , 0 , 0 ] [ 0 , 1 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]; 
 removing <Marked_a(a(f(x,y))),Marked_f(a(b(a(b(a(x))))),a(b(a(b(a(y))))))>
 [ {
      
     DP termination of:
     <Marked_f(a(x),a(y)) , Marked_a(f(x,y))>
<Marked_f(a(x),a(y)) , Marked_f(x,y)>
<Marked_f(b(x),b(y)) , Marked_f(x,y)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(a(x),a(y)) , Marked_f(x,y)>
<Marked_f(b(x),b(y)) , Marked_f(x,y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 48.042439 seconds (real time)
Cime Exit Status: 0