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For every associative dialgebra $\\mathcal{D}$, the quotient $\\mathcal{A}_\\mathcal{D}:=\\mathcal{D}/\\mathsf{Id}(S)$, where $\\mathsf{Id}(S)$ is the ideal of $\\mathcal{D}$ generated by the set $S:=\\{x \\vdash y-x\\dashv y \\mid x,y\\in \\mathcal{D}\\}$, is called the associative algebra associated to $\\mathcal{D}$. Here we show that the Gelfand--Kirillov dimension of $\\mathcal{D}$ is bounded above by twice the Gelfand--Kirillov dimension of $\\mathcal{A}_\\mathcal{D}$. 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