Add to ORKGInternational audienceA sup-interpretation is a tool which provides upper bounds on the size of the values computed by the function symbols of a program. Sup-interpretations have shown their interest to deal with the complexity of first order functional programs. This paper is an attempt to adapt the framework of sup-interpretations to a fragment of object-oriented programs, including loop and while constructs and methods with side effects. We give a criterion, called brotherly criterion, which uses the notion of sup-interpretation to ensure that each brotherly program computes objects whose size is polynomially bounded by the inputs sizes. Moreover we give some heuristics in order to compute the sup-interpretation of a given method