Many techniques exist for statically computing properties of the evolution of processes expressed in process algebras. Static analysis has shown how to obtain useful results that can both be checked and computed in polynomial time. In this paper we develop a static analysis in relational form which substantially improves the precision of the results obtained while being able to deal with the full generality of the syntax of processes. The analysis reveals a feasible complexity for practical examples and gives rise to a fast prototype. We use this prototype to automatically prove the correct delivery of messages for the implementation of an accident service, which is based on multiplexed communication, a crucial feature of global computing applications.