Cutting a Proof into Bite-Sized Chunks: Incrementally proving termination in higher-order term rewriting (Invited Talk)

Author Cynthia Kop

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Cynthia Kop
  • Department of Software Science, Radboud University Nijmegen, The Netherlands

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Cynthia Kop. Cutting a Proof into Bite-Sized Chunks: Incrementally proving termination in higher-order term rewriting (Invited Talk). In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


This paper discusses a number of methods to prove termination of higher-order term rewriting systems, with a particular focus on large systems. In first-order term rewriting, the dependency pair framework can be used to split up a large termination problem into multiple (much) smaller components that can be solved individually. This is important because a large problem may take exponentially longer to solve in one go than solving each of its components. Unfortunately, while there are higher-order versions of several of these methods, they often fail to simplify a problem enough. Here, we will explore some of these techniques and their limitations, and discuss what else can be done to incrementally build a termination proof for higher-order systems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Equational logic and rewriting
  • Termination
  • Modularity
  • Higher-order term rewriting
  • Dependency Pairs
  • Algebra Interpretations


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