We show how confluence criteria based on decreasing diagrams are generalized to ones composable with other criteria. For demonstration of the method, the confluence criteria of orthogonality, rule labeling, and critical pair systems for term rewriting are recast into composable forms. We also show how such a criterion can be used for a reduction method that removes rewrite rules unnecessary for confluence analysis. In addition to them, we prove that Toyama's parallel closedness result based on parallel critical pairs subsumes his almost parallel closedness theorem.

翻译：我们展示了如何将基于递减图的汇流准则推广为可与其他准则组合的形式。为演示该方法，我们将项重写系统中正交性、规则标记和临界对系统的汇流准则重新表述为可组合形式。同时还证明了此类准则可应用于归约方法，以移除对汇流分析不必要的重写规则。此外，我们证明了基于并行临界对的Toyama并行封闭性结果涵括了他的几乎并行封闭性定理。