Frequent closures (FCIs) and generators (FGs) as well as the precedence relation on FCIs are key components in the definition of a variety of association rule bases. Although their joint computation has been studied in concept analysis, no scalable algorithm exists for the task at present. We propose here to reverse a method from the latter field using a fundamental property of hypergraph theory. The goal is to extract the precedence relation from a more common mining output, i.e. closures and generators. The resulting order computation algorithm proves to be highly efficient, benefiting from peculiarities of generator families in typical mining datasets. Due to its genericity, the new algorithm fits an arbitrary FCI/FG-miner.