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Repeated recursion unfolding is a new approach that repeatedly unfolds arecursion with itself and simplifies it while keeping all unfolded rules. Eachunfolding doubles the number of recursive steps covered. This reduces thenumber of recursive rule applications to its logarithm at the expense ofintroducing a logarithmic number of unfolded rules to the program. Efficiencycrucially depends on the amount of simplification inside the unfolded rules. Weprove a super-linear speedup theorem in the best case, i.e. speedup by morethan a constant factor. Our optimization can lower the time complexity class ofa program. In this paper, the super-linear speedup is within bounds: it holdsup to an arbitrary but chosen upper bound on the number of recursive steps. Wealso report on the first results with a prototype implementation of repeatedrecursion unfolding. A simple program transformation completely removesrecursion up to the chosen bound. The actual runtime improvement quicklyreaches several orders of magnitude.

Repeated Recursion Unfolding for Super-Linear Speedup within Bounds