  We study the computational complexity of reachability, coverability and
inclusion for extensions of context-free commutative grammars with integer
counters and reset operations on them. Those grammars can alternatively be
viewed as an extension of communication-free Petri nets. Our main results are
that reachability and coverability are inter-reducible and both NP-complete. In
particular, this class of commutative grammars enjoys semi-linear reachability
sets. We also show that the inclusion problem is, in general, coNEXP-complete
and already $\Pi_2^\text{P}$-complete for grammars with only one non-terminal
symbol. Showing the lower bound for the latter result requires us to develop a
novel $\Pi_2^\text{P}$-complete variant of the classic subset sum problem.
