We develop new methods to statically bound the resources needed for the execution of systems of concurrent, interactive threads. Our study is concerned with a synchronous model of interaction based on cooperative threads whose execution proceeds in synchronous rounds called instants. Our contribution is a system of compositional static analyses to guarantee that each instant terminates and to bound the size of the values computed by the system as a function of the size of its parameters at the beginning of the instant.
Our method generalises an approach designed for first-order functional languages that relies on a combination of standard termination techniques for term rewriting systems and an analysis of the size of the computed values based on the notion of quasi-interpretation. These two methods can be combined to obtain an explicit polynomial bound on the resources needed for the execution of the system during an instant.