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

TRS termination of:
[1] first(0,X) -> nil
[2] first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
[3] from(X) -> cons(X,n__from(s(X)))
[4] first(X1,X2) -> n__first(X1,X2)
[5] from(X) -> n__from(X)
[6] activate(n__first(X1,X2)) -> first(X1,X2)
[7] activate(n__from(X)) -> from(X)
[8] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
<Marked_activate(n__from(X)) , Marked_from(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)> 
      --> <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
  <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)> 
     --> <Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_activate -> 1
Marked_first -> 2

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] first(0,X) -> nil
[2] first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
[3] from(X) -> cons(X,n__from(s(X)))
[4] first(X1,X2) -> n__first(X1,X2)
[5] from(X) -> n__from(X)
[6] activate(n__first(X1,X2)) -> first(X1,X2)
[7] activate(n__from(X)) -> from(X)
[8] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
<Marked_activate(n__from(X)) , Marked_from(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_first(s(X),cons(Y,Z)) , Marked_activate(Z)>
<Marked_activate(n__first(X1,X2)) , Marked_first(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.004581 seconds (real time)
Cime Exit Status: 0