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

TRS termination of:
[1] fib(N) -> sel(N,fib1(s(0),s(0)))
[2] fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
[3] add(0,X) -> X
[4] add(s(X),Y) -> s(add(X,Y))
[5] sel(0,cons(X,XS)) -> X
[6] sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
[7] fib1(X1,X2) -> n__fib1(X1,X2)
[8] activate(n__fib1(X1,X2)) -> fib1(X1,X2)
[9] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_fib(N) , Marked_sel(N,fib1(s(0),s(0)))>
<Marked_fib(N) , Marked_fib1(s(0),s(0))>
<Marked_fib1(X,Y) , Marked_add(X,Y)>
<Marked_add(s(X),Y) , Marked_add(X,Y)>
<Marked_sel(s(N),cons(X,XS)) , Marked_sel(N,activate(XS))>
<Marked_sel(s(N),cons(X,XS)) , Marked_activate(XS)>
<Marked_activate(n__fib1(X1,X2)) , Marked_fib1(X1,X2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_sel(s(N),cons(X,XS)) , Marked_sel(N,activate(XS))> 
      --> <Marked_sel(s(N),cons(X,XS)) , Marked_sel(N,activate(XS))>
}

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

ST: Marked_sel -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_add -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] fib(N) -> sel(N,fib1(s(0),s(0)))
[2] fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
[3] add(0,X) -> X
[4] add(s(X),Y) -> s(add(X,Y))
[5] sel(0,cons(X,XS)) -> X
[6] sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
[7] fib1(X1,X2) -> n__fib1(X1,X2)
[8] activate(n__fib1(X1,X2)) -> fib1(X1,X2)
[9] activate(X) -> X
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_fib(N) , Marked_sel(N,fib1(s(0),s(0)))>
<Marked_fib(N) , Marked_fib1(s(0),s(0))>
<Marked_fib1(X,Y) , Marked_add(X,Y)>
<Marked_add(s(X),Y) , Marked_add(X,Y)>
<Marked_sel(s(N),cons(X,XS)) , Marked_sel(N,activate(XS))>
<Marked_sel(s(N),cons(X,XS)) , Marked_activate(XS)>
<Marked_activate(n__fib1(X1,X2)) , Marked_fib1(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_sel(s(N),cons(X,XS)) , Marked_sel(N,activate(XS))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_add(s(X),Y) , Marked_add(X,Y)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.007444 seconds (real time)
Cime Exit Status: 0