  In this paper, we prove the conjecture of Demyanov and Ryabova on the length
of cycles in converting exhausters in an affinely independent setting and
obtain a combinatorial reformulation of the conjecture.
  Given a finite collection of polyhedra, we can obtain its "dual" collection
by forming another collection of polyhedra, which are obtained as the convex
hull of all support faces of all polyhedra for a given direction in space. If
we keep applying this process, we will eventually cycle due to the finiteness
of the problem. Demyanov and Ryabova claim that this cycle will eventually
reach a length of at most two.
  We prove that the conjecture is true in the special case, that is, when we
have affinely independent number of vertices in the given space. We also obtain
an equivalent combinatorial reformulation for the problem, which should advance
insight for the future work on this problem.
