  For any Kac-Moody root data $\mathcal D$, D. Muthiah and D. Orr have defined
a partial order on the semi-direct product $W^+$ of the integral Tits cone with
the vectorial Weyl group of $\mathcal D$, and a strictly compatible $\mathbb
Z$-valued length function. We classify covers for this order and show that this
length function defines a $\mathbb Z$-grading of $W^+$, generalizing the case
of affine ADE root systems and giving a positive answer to a conjecture of
Muthiah and Orr.
