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TA4SP is a state-of-art tool of AVISPA that can automatically verify security protocol with unbounded number of parallel sessions. But it still has some limitations and can't verify hierarchy of authentication automatically. In this paper, we use an approximation-based model to define security protocol and design an algorithm close to the real implementation to calculate the fix-point tree automata based on the tool TA4SP. A method is proposed for analyzing hierarchy of authentication properties as extension of TA4SP. We illustrate the effectiveness of this model with the example of NSPK protocol.