  In this paper the concept of Parikh-reducing Church-Rosser systems is
studied. It is shown that for two classes of regular languages there exist such
systems which describe the languages using finitely many equivalence classes of
the rewriting system. The two classes are: 1.) the class of all regular
languages such that the syntactic monoid contains only abelian groups and 2.)
the class of all group languages over a two-letter alphabet. The construction
of the systems yield a monoid representation such that all subgroups are
abelian. Additionally, the complexity of those representations is studied.
