Context Dependent Interpretations

Context-dependent interpretations are a termination proof method developed by Hofbauer in 2001. They extend the interpretations into F-algebras by introducing an additional parameter to the interpretation functions. The additional parameter is changed by the context of the evaluated subterm, thus giving rise to the name “context-dependent interpretations”. They were designed to give good upper bounds on the derivation height of terms with respect to rewrite systems. In this thesis, the algorithm of Contejean, Marché, Tomás, and Urbain for automatically finding polynomials interpretations to prove termination of rewrite systems is adapted to context-dependent interpretations. We will describe our implementation of this adaptation. Furthermore, we will present a subclass of context-dependent interpretations which induces a quadratic upper bound on the derivational complexity of the considered rewrite system. Finding context-dependent interpretations of this subclass is also part of the implementation, for which we will present some experimental results.