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

TRS termination of:
[1] a__first(0,X) -> nil
[2] a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
[3] a__from(X) -> cons(mark(X),from(s(X)))
[4] mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
[5] mark(from(X)) -> a__from(mark(X))
[6] mark(0) -> 0
[7] mark(nil) -> nil
[8] mark(s(X)) -> s(mark(X))
[9] mark(cons(X1,X2)) -> cons(mark(X1),X2)
[10] a__first(X1,X2) -> first(X1,X2)
[11] a__from(X) -> from(X)


Sub problem: 
guided: 

DP termination of:
<Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)>
<Marked_a__from(X) , Marked_mark(X)>
<Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
<Marked_mark(from(X)) , Marked_a__from(mark(X))>
<Marked_mark(from(X)) , Marked_mark(X)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
      --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(from(X)) , Marked_mark(X)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(from(X)) , Marked_a__from(mark(X))>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(cons(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(from(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(from(X)) , Marked_a__from(mark(X))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(from(X)) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(from(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(from(X)) , Marked_mark(X)> 
     --> <Marked_mark(from(X)) , Marked_mark(X)>
  <Marked_mark(from(X)) , Marked_mark(X)> 
     --> <Marked_mark(from(X)) , Marked_a__from(mark(X))>
  <Marked_mark(from(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(from(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(from(X)) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(from(X)) , Marked_a__from(mark(X))> 
     --> <Marked_a__from(X) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(from(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(from(X)) , Marked_a__from(mark(X))>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(from(X)) , Marked_mark(X)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(from(X)) , Marked_a__from(mark(X))>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(first(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))> 
     --> <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)>
  <Marked_a__from(X) , Marked_mark(X)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_a__from(X) , Marked_mark(X)> --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__from(X) , Marked_mark(X)> 
     --> <Marked_mark(from(X)) , Marked_mark(X)>
  <Marked_a__from(X) , Marked_mark(X)> 
     --> <Marked_mark(from(X)) , Marked_a__from(mark(X))>
  <Marked_a__from(X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__from(X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__from(X) , Marked_mark(X)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(from(X)) , Marked_mark(X)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(from(X)) , Marked_a__from(mark(X))>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X2)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_mark(X1)>
  <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)> 
     --> <Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  a__first(0,X) >= nil ;
  a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z)) ;
  a__first(X1,X2) >= first(X1,X2) ;
  mark(nil) >= nil ;
  mark(0) >= 0 ;
  mark(cons(X1,X2)) >= cons(mark(X1),X2) ;
  mark(first(X1,X2)) >= a__first(mark(X1),mark(X2)) ;
  mark(s(X)) >= s(mark(X)) ;
  mark(from(X)) >= a__from(mark(X)) ;
  a__from(X) >= cons(mark(X),from(s(X))) ;
  a__from(X) >= from(X) ;
  Marked_a__from(X) >= Marked_mark(X) ;
  Marked_a__first(s(X),cons(Y,Z)) >= Marked_mark(Y) ;
  Marked_mark(cons(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(first(X1,X2)) >= Marked_a__first(mark(X1),mark(X2)) ;
  Marked_mark(first(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(first(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(from(X)) >= Marked_a__from(mark(X)) ;
  Marked_mark(from(X)) >= Marked_mark(X) ;
 }
 + Disjunctions:{ 
{
  Marked_a__from(X) > Marked_mark(X) ;
 }
{
  Marked_a__first(s(X),cons(Y,Z)) > Marked_mark(Y) ;
 }
{
  Marked_mark(cons(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_a__first(mark(X1),mark(X2)) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(first(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(from(X)) > Marked_a__from(mark(X)) ;
 }
{
  Marked_mark(from(X)) > Marked_mark(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: a__first(0,X) >= nil
constraint: a__first(s(X),cons(Y,Z)) >= cons(mark(Y),first(X,Z))
constraint: a__first(X1,X2) >= first(X1,X2)
constraint: mark(nil) >= nil
constraint: mark(0) >= 0
constraint: mark(cons(X1,X2)) >= cons(mark(X1),X2)
constraint: mark(first(X1,X2)) >= a__first(mark(X1),mark(X2))
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(from(X)) >= a__from(mark(X))
constraint: a__from(X) >= cons(mark(X),from(s(X)))
constraint: a__from(X) >= from(X)
constraint: Marked_a__from(X) >= Marked_mark(X)
constraint: Marked_a__first(s(X),cons(Y,Z)) >= Marked_mark(Y)
constraint: Marked_mark(cons(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(first(X1,X2)) >= Marked_a__first(mark(X1),mark(X2))
constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(first(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(from(X)) >= Marked_a__from(mark(X))
constraint: Marked_mark(from(X)) >= Marked_mark(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__first(0,X) -> nil
[2] a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
[3] a__from(X) -> cons(mark(X),from(s(X)))
[4] mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
[5] mark(from(X)) -> a__from(mark(X))
[6] mark(0) -> 0
[7] mark(nil) -> nil
[8] mark(s(X)) -> s(mark(X))
[9] mark(cons(X1,X2)) -> cons(mark(X1),X2)
[10] a__first(X1,X2) -> first(X1,X2)
[11] a__from(X) -> from(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)>
<Marked_a__from(X) , Marked_mark(X)>
<Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
<Marked_mark(from(X)) , Marked_a__from(mark(X))>
<Marked_mark(from(X)) , Marked_mark(X)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__first(s(X),cons(Y,Z)) , Marked_mark(Y)>
<Marked_a__from(X) , Marked_mark(X)>
<Marked_mark(first(X1,X2)) , Marked_a__first(mark(X1),mark(X2))>
<Marked_mark(first(X1,X2)) , Marked_mark(X1)>
<Marked_mark(first(X1,X2)) , Marked_mark(X2)>
<Marked_mark(from(X)) , Marked_a__from(mark(X))>
<Marked_mark(from(X)) , Marked_mark(X)>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_mark(cons(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ nil ] () = 0; 
 [ a__from ] (X0) = 3*X0 + 3; 
 [ mark ] (X0) = 3*X0 + 1; 
 [ 0 ] () = 0; 
 [ Marked_a__first ] (X0,X1) = 3*X1 + 1*X0; 
 [ s ] (X0) = 2*X0 + 1; 
 [ a__first ] (X0,X1) = 3*X1 + 1*X0 + 3; 
 [ Marked_a__from ] (X0) = 3*X0 + 3; 
 [ first ] (X0,X1) = 3*X1 + 1*X0 + 3; 
 [ cons ] (X0,X1) = 1*X0 + 2; 
 [ Marked_mark ] (X0) = 3*X0 + 3; 
 [ from ] (X0) = 3*X0 + 2; 
 removing <Marked_a__first(s(X),cons(Y,Z)),Marked_mark(Y)><Marked_mark(
                                                            first(X1,
                                                             X2)),Marked_a__first(
                                                                   mark(
                                                                    X1),
                                                                   mark(X2))><
Marked_mark(first(X1,X2)),Marked_mark(X1)><Marked_mark(first(X1,X2)),
Marked_mark(X2)><Marked_mark(from(X)),Marked_a__from(mark(X))><Marked_mark(
                                                                from(
                                                                 X)),
Marked_mark(X)><Marked_mark(s(X)),Marked_mark(X)><Marked_mark(cons(X1,X2)),
Marked_mark(X1)>
 [ {
      
     DP termination of:
     <Marked_a__from(X) , Marked_mark(X)>
 ,
 CRITERION: SG
 [  ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.070034 seconds (real time)
Cime Exit Status: 0