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

TRS termination of:
[1] f(X) -> cons(X,n__f(g(X)))
[2] g(0) -> s(0)
[3] g(s(X)) -> s(s(g(X)))
[4] sel(0,cons(X,Y)) -> X
[5] sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
[6] f(X) -> n__f(X)
[7] activate(n__f(X)) -> f(X)
[8] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_f(X) , Marked_g(X)>
<Marked_g(s(X)) , Marked_g(X)>
<Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))>
<Marked_sel(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_activate(n__f(X)) , Marked_f(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))> 
      --> <Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))>
}

{  <Marked_g(s(X)) , Marked_g(X)> --> <Marked_g(s(X)) , Marked_g(X)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  g(s(X)) >= s(s(g(X))) ;
  g(0) >= s(0) ;
  f(X) >= cons(X,n__f(g(X))) ;
  f(X) >= n__f(X) ;
  sel(s(X),cons(Y,Z)) >= sel(X,activate(Z)) ;
  sel(0,cons(X,Y)) >= X ;
  activate(n__f(X)) >= f(X) ;
  activate(X) >= X ;
  Marked_sel(s(X),cons(Y,Z)) >= Marked_sel(X,activate(Z)) ;
 }
 + Disjunctions:{ 
{
  Marked_sel(s(X),cons(Y,Z)) > Marked_sel(X,activate(Z)) ;
 }
 } 
=== 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 ===
=== STOPING TIMER virtual ===
constraint: g(s(X)) >= s(s(g(X)))
constraint: g(0) >= s(0)
constraint: f(X) >= cons(X,n__f(g(X)))
constraint: f(X) >= n__f(X)
constraint: sel(s(X),cons(Y,Z)) >= sel(X,activate(Z))
constraint: sel(0,cons(X,Y)) >= X
constraint: activate(n__f(X)) >= f(X)
constraint: activate(X) >= X
constraint: Marked_sel(s(X),cons(Y,Z)) >= Marked_sel(X,activate(Z))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  g(s(X)) >= s(s(g(X))) ;
  g(0) >= s(0) ;
  f(X) >= cons(X,n__f(g(X))) ;
  f(X) >= n__f(X) ;
  sel(s(X),cons(Y,Z)) >= sel(X,activate(Z)) ;
  sel(0,cons(X,Y)) >= X ;
  activate(n__f(X)) >= f(X) ;
  activate(X) >= X ;
  Marked_g(s(X)) >= Marked_g(X) ;
 }
 + Disjunctions:{ 
{
  Marked_g(s(X)) > Marked_g(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
=== 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 ===
=== STOPING TIMER virtual ===
constraint: g(s(X)) >= s(s(g(X)))
constraint: g(0) >= s(0)
constraint: f(X) >= cons(X,n__f(g(X)))
constraint: f(X) >= n__f(X)
constraint: sel(s(X),cons(Y,Z)) >= sel(X,activate(Z))
constraint: sel(0,cons(X,Y)) >= X
constraint: activate(n__f(X)) >= f(X)
constraint: activate(X) >= X
constraint: Marked_g(s(X)) >= Marked_g(X)
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] f(X) -> cons(X,n__f(g(X)))
[2] g(0) -> s(0)
[3] g(s(X)) -> s(s(g(X)))
[4] sel(0,cons(X,Y)) -> X
[5] sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
[6] f(X) -> n__f(X)
[7] activate(n__f(X)) -> f(X)
[8] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_f(X) , Marked_g(X)>
<Marked_g(s(X)) , Marked_g(X)>
<Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))>
<Marked_sel(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_activate(n__f(X)) , Marked_f(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { cons  <  f ; cons  <  sel ;
                                   cons  <  activate ; cons  <  Marked_sel ;
                                   n__f  <  f ; n__f  <  sel ;
                                   n__f  <  activate ; n__f  <  Marked_sel ;
                                   g  <  f ; g  >  s ; g  <  sel ;
                                   g  <  activate ; g  <  Marked_sel ;
                                   f  >  cons ; f  >  n__f ; f  >  g ;
                                   f  >  s ; f  <  sel ; f  <  activate ;
                                   f  <  Marked_sel ; s  <  g ; s  <  f ;
                                   s  <  sel ; s  <  activate ;
                                   s  <  Marked_sel ; sel  >  cons ;
                                   sel  >  n__f ; sel  >  g ; sel  >  f ;
                                   sel  >  s ; sel  >  activate ;
                                   activate  >  cons ; activate  >  n__f ;
                                   activate  >  g ; activate  >  f ;
                                   activate  >  s ; activate  <  sel ;
                                   activate  <  Marked_sel ;
                                   Marked_sel  >  cons ; Marked_sel  >  n__f ;
                                   Marked_sel  >  g ; Marked_sel  >  f ;
                                   Marked_sel  >  s ; Marked_sel  >  activate ;
                                   }

 ]} 
{
 
DP termination of:
<Marked_g(s(X)) , Marked_g(X)>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     RPO with AFS = AFS: 
     and precedence:
     prec (All symbols are Lex.): { cons  <  f ; cons  <  sel ;
                                   cons  <  activate ; n__f  <  f ;
                                   n__f  <  sel ; n__f  <  activate ; 
                                   g  <  f ; g  >  s ; g  <  sel ;
                                   g  <  activate ; f  >  cons ; f  >  n__f ;
                                   f  >  g ; f  >  s ; f  <  sel ;
                                   f  <  activate ; s  <  g ; s  <  f ;
                                   s  <  sel ; s  <  activate ; sel  >  cons ;
                                   sel  >  n__f ; sel  >  g ; sel  >  f ;
                                   sel  >  s ; sel  >  activate ;
                                   activate  >  cons ; activate  >  n__f ;
                                   activate  >  g ; activate  >  f ;
                                   activate  >  s ; activate  <  sel ; }

 ]} 
 ]} 
 ]} 

Cime worked for 0.073483 seconds (real time)
Cime Exit Status: 0