(**************************************************************)
(*   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          *)
(**************************************************************)
From Undecidability.Shared.Libs.DLW
From Undecidability.PCP              Require Import PCP PCP_undec.
From Undecidability.StackMachines    Require Import BSM.
From Undecidability.MinskyMachines   Require Import MM.
From Undecidability.ILL
(* The reduction chain from the CPP 2019, Y. Forster & D. Larchey-Wendling *)

Theorem PCP_chain_ILL :
⎩ PCP ⪯ₘ PCPb ⪯ₘ iPCPb ⪯ₘ BSM_HALTING ⪯ₘ MM_HALTS_ON_ZERO ⪯ₘ EILL_PROVABILITY ⪯ₘ ILL_PROVABILITY ⎭.