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Model composition helps designers managing complexities by modeling different system views separately, and later compose them into an integrated model. In the past years, researchers have focused on the definition of model composition approaches (operators) and the tools supporting them (model composition engines). Testing model composition engines is hard. It requires the synthesis and analysis of complex data structures (models). In this context, synthesis means to assembly complex structures in a coherent way with respect to semantic constraints. In this paper we propose to automatically synthesize input data for model composition engines using a model decomposition operator. Through this operator we synthesize models in a coherent way, satisfying semantic constraints and taking into account the complex mechanics involved in the model composition. Furthermore, such operator enables a straightforward analysis of the composition result. [ABSTRACT FROM AUTHOR]