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We prove that ${\\rm rep.dim}\\ T_2(A)$ is at most three if $A$ is Dynkin type and ${\\rm rep.dim}\\ T_2(A)$ is at most four if $A$ is not Dynkin type. Let $T$ be a tilting A-$\\module$ and $\\ol{T}=T\\oplus\\ol{P}$ be a tilting $A^{(1)}$-$\\module$. 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