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Summary: Automatic Inference of Upper Bounds for
Recurrence Relations in Cost Analysis
Elvira Albert1
, Puri Arenas1
, Samir Genaim2
, and Germ´an Puebla2
1
DSIC, Complutense University of Madrid, E-28040 Madrid, Spain
2
CLIP, Technical University of Madrid, E-28660 Boadilla del Monte, Madrid, Spain
Abstract. The classical approach to automatic cost analysis consists of
two phases. Given a program and some measure of cost, we first pro-
duce recurrence relations (RRs) which capture the cost of our program
in terms of the size of its input data. Second, we convert such RRs into
closed form (i.e., without recurrences). Whereas the first phase has re-
ceived considerable attention, with a number of cost analyses available
for a variety of programming languages, the second phase has received
comparatively little attention. In this paper we first study the features
of RRs generated by automatic cost analysis and discuss why existing
computer algebra systems are not appropriate for automatically obtain-
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