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Frequent tree patterns have many applications in different domains such as XML document mining, user web log analysis, network routing and bioinformatics. In this paper, we first introduce three new tree encodings and accordingly present an efficient algorithm for finding frequent patterns from rooted unordered trees with the assumption that children of every node in database trees are identically labeled. Then, we generalize the method and propose the UITree algorithm to find frequent patterns from rooted unordered trees without any restriction. Compared to other algorithms in the literature, UItree manages occurrences of a candidate tree in database trees more efficiently. Our extensive experiments on both real and synthetic datasets show that UITree significantly outperforms the most efficient existing works on mining unordered trees.