  In this paper we investigate the number of objects actually used in the
terminating computations of a certain variant of polarizationless P systems
with active membranes. The P systems we consider here have no in-communication
rules and have no different rules triggered by the same object to manipulate
the same membrane. We show that if we consider such a P system $\Pi$ and its
terminating computation $\cal C$, then we can compute the result of $\cal C$ by
setting a polynomial upper bound on the content of each region in $\cal C$.
