Outermost Termination via Contextual Dependency Pairs

Recently, the problem of proving outermost termination has been addressed mainly by methods relying on transformations ([4, 1, 3]). Here we describe a more direct approach inspired by the dependency pair (DP) framework of [2]. The basic idea is to enrich dependency pairs by an additional component, namely the calling context of the corresponding recursive function call. Then one can use the additional contextual information to model DP chains adhering to certain strategies (e.g. the outermost strategy). Additionally, existing methods of the ordinary DP approach can partly be reused. Building upon this framework of contextual DPs, we describe a DP processor exploiting the additional contextual information. Basically, this processor analyzes nested contexts accumulated by consecutive DPs on DP chain candidates for (certain) redexes. If such a redex is found, the chain candidate is not a proper chain. Finally, we provide some empirical evaluation of our approach.