Section Motivation.
Variable (n: nat).
Implicit Type (m p: nat) (M N: list (nat * nat)).
Definition step '(a, b) := (n + a, 1 + b).
Notation Step X := (map step X).
Definition t k := (k * n, k).
Definition T k := tab t k.
Definition Mrel m p M := M ++ [(p, m)] = t 0 :: Step M.

Lemma M_backward_exists m p M: Mrel m p M -> exists l, M = T l.