2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62945The (.)_reg construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)_reg which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J-order structure). We show that (S)_reg can be described by a rather simple complete string rewrite system, as a consequence of which we obtain a new proof of the normal form theorem for (S)_reg. The new proof of the normal form theorem is conceptually simpler than the previous proofs.Group Theory29M05; 20M17; 68W30text