A $2$-complex with contracting non-positive immersions and positive maximal irreducible curvature

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.