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We design a meta-algorithm that allows to solve both problems in time $2^{O(rw^3)}\\cdot n^{4}$, $2^{O(q^2\\log(q))}\\cdot n^{4}$, and $n^{O(k^2)}$ where $rw$ is the rank-width, $q$ the $\\mathbb{Q}$-rank-width, and $k$ the mim-width of a given decomposition. This answers in the affirmative an open question raised by Jaffke et al. 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