Definition reduction_reach_rewrite (p: conf * conf) :=
let (c1,c2) := p in (TMrules, mk_srconf c1, mk_srconf c2).
End Fix_TM.

Theorem reduction_reach_sr : Reach ⪯ SR_fin.
Definition trans_R (Sigma : finType) (R : srs Sigma) :=
map (fun '(x,y) => (map (@index Sigma) x, map (@index Sigma) y)) R.