Section SR_to_MPCP.
Local Definition string := string nat.
Variable R : stack nat.
Variables x0 y0 : string.
Notation "x ≻ y" := (rew R x y) (at level 70).
Notation "x ≻* y" := (rewt R x y) (at level 70).
Notation Sigma := (x0 ++ y0 ++ sym R).
Definition dollar := fresh Sigma.
Notation "$" := dollar.
Definition hash := fresh (dollar :: Sigma).
Notation "#" := hash.

Lemma sep_doll : $ <> #.