Exercise 8, § 4

Let $R_1$ and $R_2$ be two irreducible reduced root systems. Show that if $W(R_1)$ and $W(R_2)$ have the same order, $R_1$ is isomorphic to $R_2$ or $R_2^-$. (Use the classification.) Does this result still hold without the assumption that $R_1$ is irreducible?