Skew and ω-Skew Confluence and Infinite Normal Forms

The notion of skew confluence was introduced to characterize non-confluent term rewriting systems that had unique infinite normal forms or Böhm like trees. This notion however is not expressive enough to deal with all possible sources of non-confluence in the context of infinite terms or terms extended with letrec. To that end, we present a new notion called ω-skew confluence. We show that ω-skew confluence constitutes a sufficient and necessary condition for uniqueness of infinite normal forms over infinite terms or terms with letrec.