  This paper shows how to obtain the key concepts and notations of Garside
theory by using the Composition--Diamond lemma. We also show in some cases the
greedy normal form is exactly a Gr\"obner--Shirshov normal form and a family of
a left-cancellative category is a Garside family, if and only if a suitable set
of reductions is confluent up to some congruence on words.
