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The results of a search engine can be improved by consulting auxiliary data. In a search database system, the association between the user query and the auxiliary data is driven by rewrite rules that augment the user query with a set of alternative queries. This paper develops a framework that formalizes the notion of a rewrite program, which is essentially a collection of hedge-rewriting rules. When applied to a search query, the rewrite program produces a set of alternative queries that constitutes a least fixpoint (lfp). The main focus of the paper is on the lfp-convergence of a rewrite program, where a rewrite program is lfp-convergent if the least fixpoint of every search query is finite. Determining whether a given rewrite program is lfp-convergent is undecidable; to accommodate that, the paper proposes a safety condition, and shows that safety guarantees lfp-convergence, and that safety can be decided in polynomial time. The effectiveness of the safety condition in capturing lfp-convergence is illustrated by an application to a rewrite program in an implemented system that is intended for widespread use.