Mayr and Meyer found ideals J(n,d) (in a polynomial ring in 10n+2
variables over a field k and generators of degree at most d+2) with ideal
membership property which is doubly exponential in n. This paper is a first
step in understanding the primary decomposition of these ideals: it is proved
here that J(n,d) has nd2+20 minimal prime ideals. Also, all the minimal
components are computed, and the intersection of the minimal components as
well