algebraic number theory – If $a_{1}=f(x)$ and $a_{r}=f(a_{r-1})$ for $r>1$ then is it true that $$limsup_{rtoinfty}gamma(a_{r})rightarrowinfty?$$

Let $f(x)$ be a polynomial with integral coefficients and $deg(f)geq 2$.we define $gamma(g(x))$ to be the degree of the polynomial $r(x)$ which divides $g(x)$ and also has minimal degree.

For $rgeq 1$, We define the sequence $a_{r}$ of polynomials as follows:

$clubsuit)a_{1}=f(x)$

$clubsuit)a_{r}=f(a_{r-1})$ for $rgeq 2$

Then is it true that
$$limsup_{rtoinfty}gamma(a_{r})rightarrowinfty?$$