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We answer positively this open question raised by Lutz and others: we show that there exists an infinite word $w$ such that $\\rho_{sup}(w)=0$ but $\\rho_{inf}(0w)>0$, where $\\rho_{sup}$ and $\\rho_{inf}$ are respectively the $\\limsup$ and the $\\liminf$ of the compression ratios $\\rho$ of the prefixes. 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