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[en] Process definition on the basis of graph transformation systems was introduced by the concept of occurrence grammars, which are a generalization of Petri net processes given by occurrence nets. Recently, subobject transformation systems were proposed as abstract framework for occurrence grammars in adhesive categories, but they are still restricted to injective matches for graph transformation steps. In this paper we review the construction of STSs as processes for plain graph grammars and discuss an extension to attributed graph grammars with non-injective matches. This is the basis for a forthcoming formal treatment in the framework of adhesive categories.