Complexity Analysis of Term Rewriting Based on Matrix and Context Dependent Interpretations

For a given (terminating) term rewriting system one can often estimate its emph{derivational complexity} indirectly by looking at the proof method that established termination. In this spirit we investigate two instances of the interpretation method: emph{matrix interpretations} and emph{context dependent interpretations}. We introduce a subclass of matrix interpretations, denoted as emph{triangular matrix interpretations}, which induce polynomial derivational complexity and establish tight correspondence results between a subclass of context dependent interpretations and restricted triangular matrix interpretations. The thus obtained new results are easy to implement and considerably extend the analytic power of existing results. We provide ample numerical data for assessing the viability of the method