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.

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