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Tree pattern matching is a fundamental operation that is used in a number of programming tasks such as mechanical theorem proving, term rewriting, symbolic computation, and nonprocedural programming languages. In this paper, we present new sequential algorithms for nonlinear pattern matching in trees. Our algorithm improves upon know tree pattern matching algorithms in important aspects such as time performance, ease of integration with several reduction strategies and ability to avoid unnecessary computation steps on match attempts that fail. The expected time complexity of our algorithm is linear in the sum of the sizes of the two trees.