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A Tool for Calculating Exponential Run-Time Properties

Affine size-change analysis has been used for calculating precise polynomial bounds on the run times, and stack depths of affine size-change terminating programs. Such polynomial costs may be discovered by a characterization as a problem in quantifier elimination. In this paper we extend this work to cover a class of exponential cost programs. The tool described allows the calculation of run-time and stack-depth costs for some classes of exponential-cost programs, again by using quantifier elimination. The technique is automated, and uses the reduce computer algebra system.