We address in this paper the problem of statically determining whether a JavaCard applet may produce a memory overflow because of the dynamic instantiation of classes inside cycles. We provide a constraint-based algorithm which determines potential loops and (mutually) recursive methods. The algorithm operates on the byte-code of an applet. It is written as a set of rules -one for each byte-code instruction- which allows a compositional reasoning and it comprises both inter- and intra-procedural analysis. We aimed at an algorithm suitable to be fed into the proof assistant Coq in order to extract a certified memory usage analyser. We prove termination of the algorithm as well as its soundness and completeness with respect to an abstraction of the operational semantics of the language.