  A new construction of a free inverse semigroup was obtained by Poliakova and
Schein in 2005. Based on their result, we find a Groebner-Shirshov basis of a
free inverse semigroup relative to the deg-lex order of words. In particular,
we give the (unique and shortest) Groebner-Shirshov normal forms in the classes
of equivalent words of a free inverse semigroup together with the
Groebner-Shirshov algorithm to transform any word to its normal form.
