There exist powerful techniques to infer upper bounds on the innermost runtime complexity of term rewrite systems (TRSs), i.e., on the lengths of rewrite sequences that follow an innermost evaluation strategy. However, the techniques to analyze the (full) runtime complexity of TRSs are substantially weaker. In this paper, we present a sufficient criterion to ensure that the runtime complexity o...

The framework of dependency pairs allows automated termination and innermost termination proofs for many TRSs where such proofs were not possible before. In this paper we present a reenement of this framework in order to prove termination in a modular way. Our mod-ularity results signiicantly increase the class of term rewriting systems where termination resp. innermost termination can be prove...

The dependency pair approach [2, 13, 14] is a powerful technique for automated termination and innermost termination proofs of term rewrite systems (TRSs). For any TRS, it generates inequality constraints that have to be satisfied by well-founded orders. We improve the dependency pair approach by considerably reducing the number of constraints produced for (innermost) termination proofs. Moreov...

[1] A remarkable correlation between the inner edge of the outer radiation belt electrons and the innermost plasmapause location is demonstrated by using 12 years of measurements of MeV electrons from the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) and the Combined Radiation and Release Experiment Satellite (CRRES) during its entire mission (July 1990–October 1991). An empir...

We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS) whose right-hand side terms are restricted to be shallow (variables occur at depth at most one) and linear (each variable occurs at most once). Innermost termin...

Computational systems based on reducing expressions usually have a predefined reduction strategy to break down the nondeterminism which is inherent to reduction relations. The innermost strategy corresponds to call by value or eager computation, that is, the computational mechanism of several programming languages like Maude, OBJ, etc. where the arguments of a function call are always evaluated...

This article presents a way to implement many-sorted term rewriting on GPU. is done by letting the GPU repeatedly perform massively parallel evaluation of all subterms. Innermost experimentally compared with relaxed form innermost rewriting, and two different garbage collection mechanisms, remove terms that are no longer needed, discussed compared. It concluded when rewrite systems exhibit suff...

We investigate termination of rewriting computations guided by strategy annotations. We show that proofs of termination can be obtained by proving (innermost) termination of context-sensitive rewriting (CSR). Hence, we investigate how to prove innermost termination of CSR using existing methods for proving termination of CSR.