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

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


Sub problem: 
guided: 

DP termination of:
<Marked_f(a,empty) , Marked_g(a,empty)>
<Marked_f(a,cons(x,k)) , Marked_f(cons(x,a),k)>
<Marked_g(cons(x,k),d) , Marked_g(k,cons(x,d))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_f(a,cons(x,k)) , Marked_f(cons(x,a),k)> 
      --> <Marked_f(a,cons(x,k)) , Marked_f(cons(x,a),k)>
}

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

Cime worked for 0.039635 seconds (real time)
Cime Exit Status: 0