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Data provenance is information that describes how a given data item was produced. The provenance includes source and intermediate data as well as the transformations involved in producing the concrete data item. In the context of a relational databases, the source and intermediate data items are relations, tuples and attribute values. The transformations are SQL queries and/or functions on the relational data items. Existing approaches capture provenance information by extending the underlying data model. This has the intrinsic disadvantage that the provenance must be stored and accessed using a different model than the actual data. In this paper, we present an alternative approach that uses query rewriting to annotate result tuples with provenance information. The rewritten query and its result use the same model and can, thus, be queried, stored and optimized using standard relational database techniques. In the paper we formalize the query rewriting procedures, prove their correctness, and evaluate a first implementation of the ideas using PostgreSQL. As the experiments indicate, our approach efficiently provides provenance information inducing only a small overhead on normal operations.