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：我们展示了基于递减图的合流准则如何被推广为可与其他准则组合的形式。为演示这一方法，我们将术语重写中正交性、规则标号和临界对系统的合流准则重构为可组合形式。同时证明了此类准则可用于一种归约方法，该方法能够移除对合流分析不必要的重写规则。此外，我们还证明了基于平行临界对的Toyama平行封闭性结果包含了其几乎平行封闭性定理。