The Maude-NRL Protocol Analyzer (Maude-NPA) is a tool and inference system for reasoning about the security of cryptographic protocols in which the cryptosystems satisfy different equational properties. It both extends and provides a formal framework for the original NRL Protocol Analyzer, which supported equational reasoning in a more limited way. Maude-NPA supports a wide variety of algebraic properties that includes many crypto-systems of interest such as, for example, one-time pads and Diffie-Hellman. Maude-NPA, like the original NPA, looks for attacks by searching backwards from an insecure attack state, and assumes an unbounded number of sessions. Because of the unbounded number of sessions and the support for different equational theories, it is necessary to develop ways of reducing the search space and avoiding infinite search paths. As a result, we have developed a number of state space reduction techniques. In order for the techniques to prove useful, they need not only to speed up the search, but should not violate soundness so that failure to find attacks still guarantees security. In this paper we describe the state space reduction techniques we use. We also provide soundness proofs, and experimental evaluations of their effect on the performance of Maude-NPA.