  Presentations of groups by rewriting systems (that is, by monoid
presentations), have been fruitfully studied by encoding the rewriting system
in a $2$--complex -- the Squier complex -- whose fundamental groupoid then
describes the derivation of consequences of the rewrite rules. We describe a
reduced form of the Squier complex, investigate the structure of its
fundamental groupoid, and show that key properties of the presentation are
still encoded in the reduced form.
