Reaction systems, a formalism describing biochemical reactions in terms of sets of reactants, inhibitors, and products, are known to have a PSPACE-complete configuration reachability problem. We show that the complexity of the problem remains unchanged even for some classes of resource-bounded reaction systems, where we disallow either inhibitors or reactants. We also prove that the complexity decreases to NP in the specific case of inhibitorless reaction systems using only one reactant per reaction.