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

Proof:
 Containment Processor:
  loop length: 1
  terms:
   fib1(X,Y)
  context: cons(X,[])
  substitution:
   X -> Y
   Y -> add(X,Y)
  Qed