Termination analysis with interpolation-based transition invariant generation

2026-08-09

AI Summary

This work addresses the longstanding disconnect between termination and non-termination analysis in infinite-state systems by proposing a unified framework that integrates both analyses for the first time. The approach leverages Craig interpolation to generate transition invariants and employs well-founded relation reasoning to simultaneously derive certificates of termination and non-termination, enabling bidirectional guidance and sharing of intermediate results. The resulting GOLEM verification framework not only uncovers structural reasons underlying system termination but also extends safety-based techniques for non-termination analysis. Evaluated on the TermComp benchmark suite, GOLEM matches the performance of state-of-the-art tools, demonstrating the effectiveness and practicality of the proposed joint analysis strategy.

Abstract

Termination and nontermination of infinite-state systems are complementary problems that, despite their close connection, are typically addressed by separate techniques. The core idea of this paper is to connect termination and nontermination analysis, enabling the two to share intermediate results and guide one another. We present a new termination analysis approach based on the generation of well-founded transition invariants. It leverages Craig interpolation for transition invariant generation, capturing the structural reasons for termination. The proposed technique extends safety-based nontermination analysis, enabling it to prove both termination and nontermination within a unified framework. We implemented our approach in the GOLEM verification framework and evaluated it on benchmarks from the Termination Competition (TermComp). Empirical results demonstrate that combining termination and nontermination is beneficial and yields performance comparable to state-of-the-art tools.

Problem

• termination analysis
• nontermination analysis
• infinite-state systems
• transition invariants
• Craig interpolation

Innovation

• transition invariant
• Craig interpolation
• termination analysis
• nontermination analysis
• unified framework