(** To preserve non-terminating behaviours, we show that the transformed code cannot take an infinity of "zero transition" cases. We use the following [measure] function over source states, which decreases strictly in the "zero transition" case. *)
Definition measure (st: state) : nat :=
match st with
| State s f sp pc ls m => (count_gotos f pc * 2)%nat
| Block s f sp (Lbranch pc :: _) ls m => (count_gotos f pc * 2 + 1)%nat
| Block s f sp bb ls m => 0%nat
| Callstate s f ls m => 0%nat
| Returnstate s ls m => 0%nat
end.

(* Specifications: *)
Lemma match_parent_locset:
forall s ts,
list_forall2 match_stackframes s ts ->
locmap_lessdef (parent_locset s) (parent_locset ts).
Lemma tunnel_step_correct:
forall st1 t st2, step ge st1 t st2 ->
forall st1' (MS: match_states st1 st1'),
(exists st2', step tge st1' t st2' /\ match_states st2 st2')
\/ (measure st2 < measure st1 /\ t = E0 /\ match_states st2 st1')%nat.
Lemma transf_initial_states:
forall st1, initial_state prog st1 ->
exists st2, initial_state tprog st2 /\ match_states st1 st2.
Lemma transf_final_states:
forall st1 st2 r,
match_states st1 st2 -> final_state st1 r -> final_state st2 r.
Theorem transf_program_correct:
forward_simulation (LTL.semantics prog) (LTL.semantics tprog).