  In this paper we describe the method which we applied to successfully compute
the primary decomposition of a certain ideal coming from applications in
combinatorial algebra and algebraic statistics regarding conditional
independence statements with hidden variables. While our method is based on the
algorithm for primary decomposition by Gianni, Trager and Zacharias, we were
not able to decompose the ideal using the standard form of that algorithm, nor
by any other method known to us.
