Termination of Rewriting with and Automated Synthesis of Forbidden Patterns

We introduce a modified version of the well-known dependency pair framework that is suitable forthe termination analysis of rewriting under forbidden pattern restrictions. By attaching contexts todependency pairs that represent the calling contexts of the corresponding recursive function calls,it is possible to incorporate the forbidden pattern restrictions in the (adapted) notion of dependencypair chains, thus yielding a sound and complete approach to termination analysis. Building uponthis contextual dependency pair framework we introduce a dependency pair processor that simplifiesproblems by analyzing the contextual information of the dependency pairs. Moreover, we show howthis processor can be used to synthesize forbidden patterns suitable for a given term rewriting systemon-the-fly during the termination analysis.