  We prove that the $2$-complex associated to the presentation $\langle a,b
\mid b,bab^{-1}a^{-2}\rangle$ has contracting non-positive immersions and
positive maximal irreducible curvature. This example shows that the contracting
non-positive immersions property is not equivalent to the notion of
non-positive irreducible curvature, answering a question raised by H. Wilton.
