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We present a large class of security protocol abstractions with the aim of improving the scope and efficiency of verification tools. We propose typed abstractions, which transform a term's structure based on its type, and untyped abstractions, which remove atomic messages, variables, and redundant terms. Our theory improves on previous work by supporting a useful subclass of shallow subterm-convergent rewrite theories, user-defined types, and untyped variables to cover type flaw attacks. Wedoi:10.3929/ethz-a-010347780 fatcat:o7vcgg4rqbdrdmo2ry7fnabjdi