A Combination Framework for Complexity

A Combination Framework for Complexity
M. Avanzini and G. Moser
Information and Computation 248:22–55, 2016.


In this paper we present a combination framework for the automated polynomial complexity analysis of term rewrite systems. The framework covers both derivational and runtime complexity analysis, and is employed as theoretical foundation in the automated complexity tool TCT. We present generalisations of powerful complexity techniques, notably a generalisation of complexity pairs and (weak) dependency pairs. Finally, we also present a novel technique, called dependency graph decomposition, that in the dependency pair setting greatly increases modularity.


Term Rewriting, Complexity Analysis, Automation, TCT, Runtime Complexity Analysis