Proving Confluence of Term Rewriting Systems via Persistency and Decreasing Diagrams

ABSTRACT. Decreasing diagrams technique (van Oostrom, 1994) has been successfully used to prove confluence of rewrite systems in various ways; using rule-labelling (van Oostrom, 2008), it can be also applied directly to prove confluence of some linear term rewriting systems (TRSs) automatically. Some efforts for extending the rule-labelling are known, but non-left-linear TRSs are left beyond the scope. Two methods for automatically proving confluence of non-(left-)linear TRSs with the rule-labelling are given. The key idea of our methods is to combine the decreasing diagrams technique with persistency of confluence (Aoto & Toyama, 1997).