Require Import Undecidability.Synthetic.Undecidability.

From Undecidability.FRACTRAN
  Require Import FRACTRAN FRACTRAN_undec.

From Undecidability.MinskyMachines
  Require Import MMA FRACTRAN_to_MMA2 MMA2_to_MMA2_zero.

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 MMA2_HALTING_undec).
  apply MMA2_MMA2_HALTS_ON_ZERO.
Qed.

Check MMA2_HALTS_ON_ZERO_undec.