  Equational unification of two terms consists of finding a substitution that,
when applied to both terms, makes them equal modulo some equational properties.
A narrowing-based equational unification algorithm relying on the concept of
the variants of a term is available in the most recent version of Maude,
version 3.0, which provides quite sophisticated unification features. A variant
of a term t is a pair consisting of a substitution sigma and the canonical form
of tsigma. Variant-based unification is decidable when the equational theory
satisfies the finite variant property. However, this unification procedure does
not take into account constructor symbols and, thus, may compute many more
unifiers than the necessary or may not be able to stop immediately. In this
paper, we integrate the notion of constructor symbol into the variant-based
unification algorithm. Our experiments on positive and negative unification
problems show an impressive speedup.
