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This paper is devoted to a low-complexity algorithm for retiming circuits without cycles, i.e., those whose network graph is a direct acyclic graph (DAG). On one hand, DAGs have a great practical importance, as shown by the on-line arithmetic circuits used as a target application in this paper. On the other hand, retiming is a costly design optimization technique, in particular when applied to large circuits. Hence the need to design a specialized retiming algorithm to handle DAGs more efficiently than general-purpose retiming algorithms. Our algorithm dramatically improves on current solutions in the literature. We gain an order of magnitude in the worst case complexity, and we show convincing experimental results at the end of this paper