We introduce *normalised rewriting*, a new rewrite relation.
It generalises former notions of rewriting modulo *E*, dropping
some conditions on *E*. For example, *E* can now be the
theory of identity, idempotency, the theory of Abelian groups, the
theory of commutative rings. We give a new completion algorithm for
normalised rewriting. It contains as an instance the usual AC
completion algorithm, but also the well-known Buchberger's algorithm
for computing standard bases of polynomial ideals.

We investigate the particular case of completion of ground equations,
In this case we prove by a uniform method that completion modulo
*E* terminates, for some interesting *E*. As a
consequence, we obtain the decidability of the word problem for some
classes of equational theories.

We give implementation results which show the efficiency of normalised completion with respect to completion modulo AC.