  Let $K$ be an arbitrary semi-cubical set that can be embedded in a standard
cube. Using Discrete Morse Theory, we construct a CW-complex that is homotopy
equivalent to the space $\vec{P}(K)_v^w$ of directed paths between two given
vertices $v,w$ of $K$. In many cases, this construction is minimal: the cells
of the constructed CW-complex are in 1--1 correspondence with the generators of
the homology of $\vec{P}(K)_v^w$.
