  It is proved that, given a (von Neumann) regular semigroup with finitely many
left and right ideals, if every maximal subgroup is presentable by a finite
complete rewriting system, then so is the semigroup. To achieve this, the
following two results are proved: the property of being defined by a finite
complete rewriting system is preserved when taking an ideal extension by a
semigroup defined by a finite complete rewriting system; a completely 0-simple
semigroup with finitely many left and right ideals admits a presentation by a
finite complete rewriting system provided all of its maximal subgroups do.
