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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 Undecidability.Synthetic.Undecidability.

From Undecidability.FRACTRAN
  Require Import FRACTRAN FRACTRAN_undec.

From Undecidability.MinskyMachines
  Require Import MMA FRACTRAN_to_MMA2.

Lemma MMA2_HALTING_undec : undecidable MMA2_HALTING.
Proof.
  apply (undecidability_from_reducibility FRACTRAN_REG_undec).
  apply FRACTRAN_REG_MMA2_HALTING.
Qed.

Check MMA2_HALTING_undec.

Lemma MMA2_HALTS_ON_ZERO_undec : undecidable MMA2_HALTS_ON_ZERO.
Proof.
  apply (undecidability_from_reducibility FRACTRAN_REG_undec).
  apply FRACTRAN_REG_MMA2_HALTS_ON_ZERO.
Qed.

Check MMA2_HALTS_ON_ZERO_undec.