Definition reduction_reach_rewrite (p: conf * conf) :=
      let (c1,c2) := p in (TMrules, mk_srconf c1, mk_srconf c2).(** ** SR with finite types to SR *)

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

Lemma nrewt_ind_left : forall (R : SRS) s (P : string -> Prop), (P s) -> (forall y z : string, rewt R s y -> rew R y z -> P y -> P z) -> forall s0 : string, rewt R s s0 -> P s0.