Section Transport.
(* Assume that P reaches a halting configuration from (0, 1) after NP steps, show that M is uniformly bounded. *)
Variable NP : nat. (* number of steps  *)
Variable NP_spec : CM.halting P (Nat.iter NP (CM.step P) cm_start).
Definition cm_end := Nat.iter NP (CM.step P) cm_start. (* final configuration *)
Definition CP : nat := CM.value cm_end. (* final counter value *)
Definition maybe_goto_1_time := (goto_time CP TP + NP * step_time CP TP + 2).
Definition maybe_index_try_stop_time :=
(NP * step_time CP TP + 2*maybe_goto_1_time + 1 + ((G + CP + 2) * (2 * goto_time CP TP + 3))).

Lemma maybe_index_try_stop l m z T : maybe_index_try_stop_time <= T ->
maybe_reachable T ([§1] ++ l, §0^1 ++ [§1] ++ §0^m, '#?0) z.