Problem:
 tail(cons(X)) -> XS
 pairNs() -> cons(0())
 oddNs() -> incr(pairNs())
 incr(cons(X)) -> cons(s(X))
 take(0(),XS) -> nil()
 take(s(N),cons(X)) -> cons(X)
 zip(nil(),XS) -> nil()
 zip(X,nil()) -> nil()
 zip(cons(X),cons(Y)) -> cons(pair(X,Y))
 repItems(nil()) -> nil()
 repItems(cons(X)) -> cons(X)

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