Termination by Absence of Infinite Chains of Dependency Pairs
نویسنده
چکیده
A technique to prove termination of term rewrite systems, or more precise, constructorsystems (CSs) is presented.Soundnessof this technique is proved and it is described how the technique can be performed automatically for a subclass of the CSs. Whereas simplification orders fail in proving termination of CSs that are not simply terminating, the presented technique may still automatically prove termination of these CSs.
منابع مشابه
On Dependency Pair Method for Proving Termination of Higher-Order Rewrite Systems
This paper explores how to extend the dependency pair technique for proving termination of higher-order rewrite systems. In the first order case, the termination of term rewriting systems are proved by showing the non-existence of an infinite R-chain of the dependency pairs. However, the termination and the non-existence of an infinite R-chain do not coincide in the higher-order case. We introd...
متن کاملTermination of Narrowing Using Dependency Pairs
In this work, we extend the dependency pair approach for automated proofs of termination in order to automate the termination proofs of narrowing. Narrowing is a generalization of term rewriting that allows free variables in terms (as in logic programming) and replaces pattern matching by syntactic unification. Narrowing has a number of important applications including execution of functional–l...
متن کاملTermination of Rewriting with and Automated Synthesis of Forbidden Patterns
We introduce a modified version of the well-known dependency pair framework that is suitable for the termination analysis of rewriting under forbidden pattern restrictions. By attaching contexts to dependency pairs that represent the calling contexts of the corresponding recursive function calls, it is possible to incorporate the forbidden pattern restrictions in the (adapted) notion of depende...
متن کاملParametrised dependency pairs for a general form of termination in annotated rewriting
We define a general form of termination, α-termination, for term rewrite systems with an annotation α. Standard termination and top-termination are particular instances. We present a variation on the dependency pair criterion of Arts and Giesl and prove that an α-annotated term rewrite system is α-terminating if and only there are no chains of α-dependency pairs. The α-dependency graphs can be ...
متن کاملTermination , AC - Termination and Dependency Pairs of Term Rewriting Systems
Recently, Arts and Giesl introduced the notion of dependency pairs, which gives effective methods for proving termination of term rewriting systems (TRSs). In this thesis, we extend the notion of dependency pairs to AC-TRSs, and introduce new methods for effectively proving AC-termination. Since it is impossible to directly apply the notion of dependency pairs to AC-TRSs, we introduce the head ...
متن کامل