Algebraic integrality of the first dynamical degree

Let $\f:\mathbb{P}^2\dashrightarrow\mathbb{P}^2$ be a rational map, and let $\lambda_1=\lim_{n\to\infty}\operatorname{deg}(\f^n)^{1/n}$ be its first dynamical degree. The algebraic-integrality conjecture. For every rational map $\f:\mathbb{P}^2\dashrightarrow\mathbb{P}^2$, the first dynamical degree $\lambda_1$ is an algebraic integer. The claim concerns the arithmetic nature of dynamical degrees; the supplied text gives no resolution evidence.