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We present a simple and effective approximated backward reachability procedure for parameterized systems with existentially and universally quantified global conditions. The individual processes operate on unbounded local variables ranging over the natural numbers. In addition, processes may communicate via broadcast, rendez-vous and shared variables. The procedure operates on an over-approximation of the transition system induced by the parameterized system. We verify mutual exclusion for complex protocols such as atomic, non-atomic and distributed versions of Lamport's bakery algorithm.