Innermost Termination of Rewrite Systems by Labeling

Semantic labeling is a powerful transformation technique for proving termination of term rewrite systems. The semantic part is given by a model or a quasi-model of the rewrite rules. A variant of semantic labeling is predictive labeling where the quasi-model condition is only required for the usable rules. In this paper we investigate how semantic and predictive labeling can be used to prove innermost termination. Moreover, we show how to reduce the set of usable rules for predictive labeling even further, both in the termination and the innermost termination case.