Generalizing Newman’s Lemma for left-linear rewrite systems

Abstract. Confluence criteria for non-terminating rewrite systems are knowntoberareandnotoriouslydifficulttoobtain.Hereweprovea new result in this direction. Our main result is a generalized version of Newman’s Lemma for left-linear term rewriting systems that does not need a full termination assumption. We discuss its relationships to previous confluence criteria, its restrictions, examples of application as well as open problems. The whole approach is developed in the (more general) framework of context-sensitive rewriting which thus turns out to be useful also for ordinary (context-free) rewriting.

Harnessing First Order Termination Provers Using Higher Order Dependency Pairs

Many functional programs and higher order term rewrite systems contain, besides higher order rules, also a significant first order part. We discuss how an automatic termination prover can split a rewrite system into a first order and a higher order part. The results are applicable to all common styles of higher order rewriting with simple types, although some dependency pair approach is needed to use them

Complete Monotonic Semantic Path Orderings

Although theoretically it is very powerful, the semantic path ordering (SPO) is not so udeful in practice, since its monotonicity has to be proved by hand for each concrete term rewrite system (TRS). In this paper we present a monotonic variation of SPO, called MSPO. It characterizes termination, i.e. a TRS is terminating if and only if ist rules are included in some MSPO. Hence MSPO is a complete termination method. On the practical side, it can be easily automated using as ingredients standard interpretations and general-purpose ordering like RPO. This is shown to be a sufficiently powerful way to handeke several non-trivial examples and to obtain methods like dummy elimination or dependency pairs (without the dependency graph refinement) as particular cases. Finally, we obtain some positive modularity results for termination based on MSPO

History of the recommended atomic-weight values from 1882 to 1997: A comparison of differences from current values to the estimated uncertainties of earlier values (Technical Report)

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Conservative Extension in Positive/Negative Conditional Term Rewriting with Applications to Software Renovation Factories

We transpose a conservative extension theorem from structural operational semantics to conditional term rewriting. The result is useful for the development of software renovation factories, and for modular specification of abstract data types

The IDA-80 measurement evaluation programme on mass spectrometric isotope dilution analysis of uranium and plutonium. Vol. 2 Preparation, characterization and transport of the test samples

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