Axiom
  Z_nat_axiom :
    forall x y : Z,
    (0 <= x)%Z ->
    (0 <= y)%Z -> (y < x)%Z -> convert_to_nat y < convert_to_nat x.

(* Specifications: *)
Lemma no_copy_succ_decreases : relation_decreases legal_config no_copy_succ no_copy_measure.