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The higher-order recursive path ordering (HORPO) defined by Jouannaud and Rubio provides a method to prove termination of higher-order rewriting. We present an iterative version of HORPO by means of an auxiliary term rewriting system, following an approach originally due to Bergstra and Klop. We study well-foundedness of the iterative definition, discuss(More)
This is a pre-publishing copy of the published paper, which includes an appendix and corrections, and is more spatially verbose in some places. All non-aesthetical changes are listed below. Rectifications Compared to the version published in Springer, this paper has some minor modifications. – In the translation of Z-TRSs to LCTRS, the sort declaration of(More)
This paper aims at developing a verification method for procedural programs via a transformation into logically constrained term rewriting systems (LCTRSs). To this end, we adapt existing rewriting induction methods to LCTRSs and propose a simple yet effective method to generalize equations. We show that we can handle realistic functions, involving, e.g.,(More)
A popular formalism of higher order rewriting, especially in the light of termination research, are the Algebraic Functional Systems (AFSs) defined by Jouannaud and Okada. However, the formalism is very permissive, which makes it hard to obtain results; consequently, techniques are often restricted to a subclass. In this paper we study(More)
Logically Constrained Term Rewriting Systems (LCTRSs) provide a general framework for term rewriting with constraints. We discuss a simple dependency pair approach to prove termination of LCTRSs. We see that existing techniques transfer to the constrained setting in a natural way. 1 Introduction In [4], logically constrained term rewriting systems are(More)
We extend the higher-order termination method of dynamic dependency pairs to Algebraic Functional Systems (AFSs). In this setting, simply typed lambda-terms with algebraic reduction and separate β-steps are considered. For left-linear AFSs, the method is shown to be complete. For so-called local AFSs we define a variation of usable rules and an extension of(More)
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(More)