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The XCS classifier system has recently shown a high degree of competence on a variety of data mining problems, but to what kind of problems XCS is well and poorly suited is seldom understood, especially for real-world classification problems. The major inconvenience has been attributed to the difficulty of determining the intrinsic characteristics of real-world classification problems. This paper investigates the domain of competence of XCS by means of a methodology that characterizes the complexity of a classification problem by a set of geometrical descriptors. In a study of 392 classification problems along with their complexity characterization, we are able to identify difficult and easy domains for XCS. We focus on XCS with hyperrectangle codification, which has been predominantly used for real-attributed domains. The results show high correlations between XCS's performance and measures of length of class boundaries, compactness of classes, and nonlinearities of decision boundaries. We also compare the relative performance of XCS with other traditional classifier schemes. Besides confirming the high degree of competence of XCS in these problems, we are able to relate the behavior of the different classifier schemes to the geometrical complexity of the problem. Moreover, the results highlight certain regions of the complexity measurement space where a classifier scheme excels, establishing a first step toward determining the best classifier scheme for a given classification problem.