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(*   Copyright Dominique Larchey-Wendling *                 *)
(*                                                            *)
(*                             * Affiliation LORIA -- CNRS  *)
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(*      This file is distributed under the terms of the       *)
(*         CeCILL v2 FREE SOFTWARE LICENSE AGREEMENT          *)
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Require Import List Arith Relations Lia.

Require Import Undecidability.Synthetic.Undecidability.

From Undecidability.Shared.Libs.DLW Require Import utils pos vec sss subcode.
From Undecidability.MinskyMachines Require Import mma_defs mma_simul.

Set Implicit Arguments.

Theorem MMA2_MMA2_HALTS_ON_ZERO : MMA2_HALTING ⪯ MMA2_HALTS_ON_ZERO.
Proof.
  apply reduces_dependent; exists.
  intros (P,v).
  destruct mma2_simulator with 1 P as (Q & HQ).
  exists (Q,v); apply HQ.
Qed.