  We give an algorithm to decide whether a given braid with four strings is a
product of three factors which are conjugates of standard generators of the
braid group. The algorithm is of polynomial time. It is based on the Garside
theory. We give also a polynomial algorithm to decide if a given braid with any
number of strings is a product of two factors which are conjugates of given
powers of the standard generators (in my previous paper this problem was solved
without polynomial estimates).
