  The (.)_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.
