Since many man-made systems consist of autonomous and interactive components, it is intrinsically difficult to analyze their abnormal behavior. The logical analysis of such a system is an indispensable process for high quality and reliable system development. In this paper, we propose an analysis method using two algebraic operations, named composition and minimization. Repetitive composition and minimization of component models with respect to a set of important events produces a new analysis model that has the same input output responses to an environment. An analysis example of the alternating bit protocol demonstrates the effectiveness of the proposed method showing that each message generated at the sender side eventually arrives to a receiver.