  We give an algorithm to decide if a given braid is a product of two factors
which are conjugates of given powers of standard generators of the braid group.
The same problem is solved in a certain class of Garside groups including
Artin-Tits groups of spherical type. The solution is based on the Garside
theory and, especially, on the theory of cyclic sliding developed by Gebhardt
and Gonzalez-Meneses. We show that if a braid is of the required form, then any
cycling orbit in its sliding circuit set in the dual Garside structure contains
an element for which this fact is immediately seen from the left normal form.
