Related papers: Termination of Cycle Rewriting by Transformation a…

We revisit the static dependency pair method for proving termination of higher-order term rewriting and extend it in a number of ways: (1) We introduce a new rewrite formalism designed for general applicability in termination proving of…

There are many techniques and tools to prove termination of C programs, but up to now these tools were not very powerful for fully automated termination proofs of programs whose termination depends on recursive data structures like lists.…

In recent years, numerous techniques were developed to automatically prove termination of different kinds of probabilistic programs. However, there are only few automated methods to disprove their termination. In this paper, we present the…

In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…

In this paper, we consider an approach introduced in term rewriting for the automatic detection of non-looping non-termination from patterns of rules. We adapt it to logic programming by defining a new unfolding technique that produces…

Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…

While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…

It has been shown that, regarding a terminating right-linear overlay term rewrite system (TRS), any rewrite sequence ending with a normal form can be simulated by the innermost reduction. In this paper, using this simulation property, we…

The term {\em meta-programming} refers to the ability of writing programs that have other programs as data and exploit their semantics. The aim of this paper is presenting a methodology allowing us to perform a correct termination analysis…

Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…

In this paper we present a new termination proof and complexity analysis of unfolding graph rewriting which is a specific kind of infinite graph rewriting expressing the general form of safe recursion. We introduce a termination order over…

Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…

Cyclic words are equivalence classes of cyclic permutations of ordinary words. When a group is given by a rewriting relation, a rewriting system on cyclic words is induced, which is used to construct algorithms to find minimal length…

This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…

Dominant sequence models like the Transformer represent structure implicitly through dense attention weights, incurring quadratic complexity. We propose RewriteNets, a novel neural architecture built on an alternative paradigm: explicit,…

In this paper, we define two particular forms of non-termination, namely loops and binary chains, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of compatibility…

We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous…

In synchronous rewriting, the productions of two rewriting systems are paired and applied synchronously in the derivation of a pair of strings. We present a new synchronous rewriting system and argue that it can handle certain phenomena…

This paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear…

We introduce a novel approach to the automated termination analysis of computer programs: we use neural networks to represent ranking functions. Ranking functions map program states to values that are bounded from below and decrease as a…