Analysing Parallel Complexity of Term Rewriting

We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool AProVE and by experiments on numerous benchmarks from the literature.Comment: Extended authors' accepted manuscript for a paper accepted for publication in the Proceedings of the 32nd International Symposium on Logic-based Program Synthesis and Transformation (LOPSTR 2022). 27 page