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Scheduling analysis for simplified distributed real-time systems, where the worst case execution time (WCET) of each task is fixed, is well understood. However, often the simplified assumption of fixed WCETs lacks accuracy, e.g. it may have a high variance depending of internal task states. Even if the transition relation of taskpsilas internal states is known, traditionally applied scalable analysis approaches cannot exploit this information in order to yield more accurate response times. In this paper we propose a new type of analysis for this kind of real-time systems. Our approach is based on a transformation of response time analysis into a satisfiability problem, enriched by task internal automata. Evaluations show the powerfulness of this analysis and, furthermore, we will exemplify how our approach can be used to analyse systems with mixed temporal and functional characterisations.