Abstract. In this paper, we present a variant of the dependency pair method for analysing runtime complexities of term rewrite systems automatically. This method is easy to implement, but signicantly extends the analytic power of existing direct methods. Our ndings extend the class of TRSs whose linear or quadratic runtime complexity can be detected automatically. We provide ample numerical data for assessing the viability of the method.

We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of first-order term rewrite systems. This is done while carefully analysing complexity preservation and reflection of the employed transformations such that the complexity of the obtained term rewrite system reflects on the complexity of the initial program. Further, we describe suitable strategies for the application of the studied transformations and provide ample experimental data for assessing the viability of our method.

Abstract. In this paper we introduce a restrictive version of the multiset path order, called polynomial path order. This recursive path order induces polynomial bounds on the maximal number of innermost rewrite steps. This result opens the way to automatically verify for a given program, written in an eager functional programming language, that the maximal number of evaluation steps starting from any function call is polynomial in the input size. To test the feasibility of our approach we have implemented this technique and compare its applicability to existing methods.

In this paper we present a combination framework for polynomial complexity analysis of term rewrite systems. The framework covers both derivational and runtime complexity analysis. 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. We employ the framework in the automated complexity tool T C T. T C T implements a majority of the techniques found in the literature, witnessing that our framework is general enough to capture a very brought setting. * This work was partially supported by FWF (Austrian Science Fund) project I-603-N18. 1 C.f. http://termcomp.uibk.ac.at/. 2 In [19] safe reductions pairs are called com-monotone reduction pairs.

No abstract