  We show that for a monic polynomial $f(x)$ over a number field $K$ containing
a global permutation polynomial of degree $>1$ as its composition factor, the
Newton Polygon of $f\mod\mathfrak p$ does not converge for $\mathfrak p$
passing through all finite places of $K$. In the rational number field case,
our result is the "only if" part of a conjecture of Wan about limiting Newton
polygons.
