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

TRS termination of:
[1] f(X) -> cons(X,n__f(n__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] g(X) -> n__g(X)
[8] activate(n__f(X)) -> f(activate(X))
[9] activate(n__g(X)) -> g(activate(X))
[10] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<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(activate(X))>
<Marked_activate(n__f(X)) , Marked_activate(X)>
<Marked_activate(n__g(X)) , Marked_g(activate(X))>
<Marked_activate(n__g(X)) , Marked_activate(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 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_activate(n__g(X)) , Marked_activate(X)> 
      --> <Marked_activate(n__g(X)) , Marked_activate(X)>
  <Marked_activate(n__g(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__f(X)) , Marked_activate(X)>
  <Marked_activate(n__f(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__g(X)) , Marked_activate(X)>
  <Marked_activate(n__f(X)) , Marked_activate(X)> 
     --> <Marked_activate(n__f(X)) , Marked_activate(X)>
}

{  <Marked_g(s(X)) , Marked_g(X)> --> <Marked_g(s(X)) , Marked_g(X)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_sel -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_activate -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_g -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
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(n__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] g(X) -> n__g(X)
[8] activate(n__f(X)) -> f(activate(X))
[9] activate(n__g(X)) -> g(activate(X))
[10] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <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(activate(X))>
<Marked_activate(n__f(X)) , Marked_activate(X)>
<Marked_activate(n__g(X)) , Marked_g(activate(X))>
<Marked_activate(n__g(X)) , Marked_activate(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sel(s(X),cons(Y,Z)) , Marked_sel(X,activate(Z))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_activate(n__f(X)) , Marked_activate(X)>
<Marked_activate(n__g(X)) , Marked_activate(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_g(s(X)) , Marked_g(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.011281 seconds (real time)
Cime Exit Status: 0