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Discovering loop structures in a process model is an important research topic for business process mining. The event logs generated in a real-life business process may be incomplete because of the missing activities. A process discovery algorithm can construct a proper process model from incomplete event logs. In this paper, an α-FL algorithm is proposed to discover a free loop structure in a process model based on Petri nets from incomplete event logs. First, repeated activities are extracted and some relations of these activities are analyzed. Then, some algorithms are designed to obtain the free loop structures. Finally, the correctness and effectiveness of the proposed approach are verified via some case studies and experiments.