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Branching bisimulation minimization is often used to obtain a smaller but equivalent model for a complicated one. It is particularly useful in compositional analysis to replace a subsystem's behaviors with the minimal one so that the growth of states can be controlled in a hierarchical, divide-and-conquer manner. Nonetheless, branching bisimulation minimization is typically invoked after the whole state space is enumerated entirely. In practice, when the parallel composition engine drains too many memory resources during exploring reachable states, it causes operating systems to swap excessively (i.e., thrashing) due to the page replacement of virtual memory. When such a scenario occurs, the system degrades dramatically in performance and becomes unusable, albeit minimization is possible to abstract the whole state space into very small one. In this paper, we present a pragmatic approach to make branching bisimulation minimization on-the-fly. It minimizes the state space during composition and releases memory resources that are no longer used. Our approach allows larger systems to be verified by taking account of operating systems memory management. [ABSTRACT FROM AUTHOR]