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We revisit parallel-innermost term rewriting as a model of parallelcomputation on inductive data structures and provide a corresponding notion ofruntime complexity parametric in the size of the start term. We proposeautomatic techniques to derive both upper and lower bounds on parallelcomplexity of rewriting that enable a direct reuse of existing techniques forsequential complexity. Our approach to find lower bounds requires confluence ofthe parallel-innermost rewrite relation, thus we also provide effectivesufficient criteria for proving confluence. The applicability and the precisionof the method are demonstrated by the relatively light effort in extending theprogram analysis tool AProVE and by experiments on numerous benchmarks from theliterature.

On Complexity Bounds and Confluence of Parallel Term Rewriting