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Acknowledgement I would like to follow the classical custom to declare that this thesis is organized and written all by myself. But, the thesis would obviously have never been finished without help from many people I am acquainted with, or things that have made me what I am. I learned analytic number theory in my bachelor years, supervised by Yoshio(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)