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Schedulability analysis for hard real-time systems requires bounds on the execution times of its tasks. To obtain useful bounds in the presence of caches, static timing analyses must predict cache hits and misses with high precision. For caches with least-recently-used (LRU) replacement policy, precise and efficient cache analyses exist. However, other widely used policies like first-in first-out (FIFO) are inherently harder to analyze. The main contributions of this paper are precise and efficient must- and may-analyses of FIFO based on the novel concept of static phase detection. The analyses statically partition sequences of memory accesses as they will occur during program execution into phases. If subsequent phases contain accesses to the same (similar) set of memory blocks, each phase contributes a bit to the overall goal of predicting hits (misses). The new must-analysis is significantly more precise than prior analyses. Both analyses can be implemented space-efficiently by sharing information using abstract LRU-stacks.