Complex services are composed of simple services which typically need to be processed in a particular order. Two complex services only match if they agree on both, their simple services and their processing order. This matching semantics can be formalized by means of modelling complex services as finite state automata (FSAs), and analysing the intersection of the FSAs. However, computing the intersection of FSAs is computationally expensive, and thus does not scale for large service repositories. This paper presents an approach for indexing and matching complex services using an abstraction that transforms the underlying FSA via its grammar into a form that can be indexed using available index mechanisms. Evaluation of this approach shows a performance gain of several orders of magnitude as compared to sequential matching.