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Analyzing Runtime Complexity via Innermost Runtime Complexity

20 pagesPublished: May 4, 2017


There exist powerful techniques to infer upper bounds on the innermost runtime complexity of term rewrite systems (TRSs), i.e., on the lengths of rewrite sequences that follow an innermost evaluation strategy. However, the techniques to analyze the (full) runtime complexity of TRSs are substantially weaker. In this paper, we present a sufficient criterion to ensure that the runtime complexity of a TRS coincides with its innermost runtime complexity. This criterion can easily be checked automatically and it allows us to use all techniques and tools for innermost runtime complexity in order to analyze (full) runtime complexity. By extensive experiments with an implementation of our results in the tool AProVE, we show that this improves the state of the art of automated complexity analysis significantly.

Keyphrases: automated complexity analysis, evaluation strategies, term rewriting

In: Thomas Eiter and David Sands (editors). LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 46, pages 249--268

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