  Divisibility monoids are a natural lattice-theoretical generalization of
Mazurkiewicz trace monoids, namely monoids in which the distributivity of the
involved divisibility lattices is kept as an hypothesis, but the relations
between the generators are not supposed to necessarily be commutations. Here,
we show that every divisibility monoid admits an explicit finite transducer
which allows to compute normal forms in quadratic time. In addition, we prove
that every divisibility monoid is biautomatic.
