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性准则如何被推广至可与其他准则组合的形式。为演示该方法，将项重写系统中正交性、规则标记及关键对系统的合流性准则重构为可组合形式。同时阐明此类准则如何用于归约方法，从而移除合流性分析中不必要的重写规则。此外，我们证明基于平行关键对的Toyama平行闭包结果蕴含其几乎平行闭包定理。