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

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


Sub problem: 
guided: 

DP termination of:
<Marked_f(empty,cons(a,k)) , Marked_f(cons(a,k),k)>
<Marked_f(cons(a,k),y) , Marked_f(y,k)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

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

{  <Marked_f(cons(a,k),y) , Marked_f(y,k)> 
      --> <Marked_f(cons(a,k),y) , Marked_f(y,k)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(empty,cons(a,k)) >= f(cons(a,k),k) ;
  f(cons(a,k),y) >= f(y,k) ;
  f(x,empty) >= x ;
  Marked_f(cons(a,k),y) >= Marked_f(y,k) ;
 }
 + Disjunctions:{ 
{
  Marked_f(cons(a,k),y) > Marked_f(y,k) ;
 }
 } 
=== 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(empty,cons(a,k)) >= f(cons(a,k),k)
constraint: f(cons(a,k),y) >= f(y,k)
constraint: f(x,empty) >= x
constraint: Marked_f(cons(a,k),y) >= Marked_f(y,k)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(x,empty) -> x
[2] f(empty,cons(a,k)) -> f(cons(a,k),k)
[3] f(cons(a,k),y) -> f(y,k)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(empty,cons(a,k)) , Marked_f(cons(a,k),k)>
<Marked_f(cons(a,k),y) , Marked_f(y,k)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(empty,cons(a,k)) , Marked_f(cons(a,k),k)>
<Marked_f(cons(a,k),y) , Marked_f(y,k)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ f ] (X0,X1) = 2*X1 + 1*X0 + 3; 
 [ cons ] (X0,X1) = 2*X1; 
 [ empty ] () = 2; 
 [ Marked_f ] (X0,X1) = 2*X1 + 1*X0; 
 removing <Marked_f(empty,cons(a,k)),Marked_f(cons(a,k),k)>
 [ {
      
     DP termination of:
     <Marked_f(cons(a,k),y) , Marked_f(y,k)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_f(cons(a,k),y) , Marked_f(y,k)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ f ] (X0,X1) = 3 + 1*X0 + 2*X1 + 0; 
 [ cons ] (X0,X1) = 3 + 1*X0 + 3*X1 + 0; 
 [ empty ] () = 2 + 0; 
 [ Marked_f ] (X0,X1) = 2*X0 + 3*X1 + 0; 
 ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.029794 seconds (real time)
Cime Exit Status: 0