Problem:
 sel(s(N),cons(X)) -> sel(N,XS)
 fib(N) -> sel(N,fib1(s(0()),s(0())))
 fib1(X,Y) -> cons(X)
 add(0(),X) -> X
 add(s(X),Y) -> s(add(X,Y))
 sel(0(),cons(X)) -> X

Proof:
 Fresh Variable Processor:
  loop length: 1
  terms:
   sel(s(N),cons(X))
  context: sel(N,[])
  substitution:
   XS -> sel(s(N),cons(X))
  Qed