During the execution of functional logic programs, particular E-uni cation problems have t o b e s o l v ed quite frequently. In this paper we c o n tribute to the e cient solution of such problems in the case where E is induced by particular term rewriting systems called macro tree transducers. We formalize the implementation of a deterministic partial E-uni cation algorithm on a deterministic abstract machine, called twin uni cation machine. The uni cation algorithm is based on a particular

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... rrowing strategy which c o m bines leftmost outermost narrowing with a local constructor consistency check and a particular occur check. The twin uni cation machine uses two runtime stacks it is an extension of an e cient leftmost outermost reduction machine for macro tree transducers. The feasibility of the presented implementation technique is proved by an implementation which has been developed on a SPARCstation SLC.