Divisibility problem for one relator monoids

We describe an algorithm which partially solves the divisibility problem for monoids with one defining relation of a special form. It can be shown that the word problem for one-relator monoids can be reduced to the problem studied here. It is conjectured that the presented algorithm can be completed to an algorithm which gives full solution of the problem. The validity of the conjecture would imply the decidability of the word problem for one-relator monoids.