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. Our approach to find lower bounds requires confluence of
the parallel-innermost rewrite relation, thus we also provide effective
sufficient criteria for proving confluence. 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: Under submission to Fundamenta Informaticae. arXiv admin note:
substantial text overlap with arXiv:2208.0100