(**************************************************************)
(*   Copyright Dominique Larchey-Wendling *                 *)
(*             Yannick Forster            +                 *)
(*                                                            *)
(*                             * Affiliation LORIA -- CNRS  *)
(*                             + Affiliation Saarland Univ. *)
(**************************************************************)
(*      This file is distributed under the terms of the       *)
(*         CeCILL v2 FREE SOFTWARE LICENSE AGREEMENT          *)
(**************************************************************)

Require Import Undecidability.Synthetic.Undecidability.

From Undecidability.MinskyMachines
  Require Import MM MM_undec.

From Undecidability.FRACTRAN
  Require Import FRACTRAN Reductions.MM_FRACTRAN.

Theorem FRACTRAN_REG_undec : undecidable FRACTRAN_REG_HALTING.
Proof.
  apply (undecidability_from_reducibility MM_HALTING_undec).
  apply MM_FRACTRAN_REG_HALTING.
Qed.

Check FRACTRAN_REG_undec.

Theorem FRACTRAN_undec : undecidable FRACTRAN_HALTING.
Proof.
  apply (undecidability_from_reducibility FRACTRAN_REG_undec).
  apply FRACTRAN_REG_FRACTRAN_HALTING.
Qed.