Transforming Derivational Complexity Of Term Rewriting To Runtime Complexity

Derivational complexity of term rewriting considers the length of the longest rewrite sequence for arbitrary start terms, whereas runtime complexity restricts start terms to basic terms. Recently, there has been notable progress in automatic inference of upper and lower bounds for runtime complexity. We propose a novel transformation that allows an off-the-shelf tool for inference of upper or lower bounds for runtime complexity to be used to determine upper or lower bounds for derivational complexity as well. Our approach is applicable to derivational complexity problems for innermost rewriting and for full rewriting. We have implemented the transformation in the tool AProVE and conducted an extensive experimental evaluation. Our results indicate that bounds for derivational complexity can now be inferred for rewrite systems that have been out of reach for automated analysis thus far.