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Is it true that :
$\forall f,g \in C([0,1],\mathbb R), \exists h \in C([0,1],[0,1])$ $f,g,h$ strictly increasing and $h([0,1])=[0,1]$ with $(f \circ h, g\circ h) \in C^{\infty}([0,1],\mathbb R)^2$?
$\forall f,g \in C([0,1],\mathbb R), \exists h \in C([0,1],[0,1])$ $f,g,h$ strictly increasing with $(f \circ h, g\circ h) \in C^{\infty}([0,1],\mathbb R)^2$?
