For $f(x, y)$ type of functions with $2$ arguments, the best way to understand the behavior of the function is to create a table or $\text{2D}$ array.
$$
\mathrm{F}(2,3)=\mathrm{F}(\mathrm{F}(1,3), 2)=\mathrm{F}(6,2)=\mathrm{F}(5,2)+1=\mathrm{F}(4,2)+1+1=. .=\mathrm{F}(1,2)+5=4+5=9
$$
Working out this complicated description, $\mathrm{F}(2,2)=\mathrm{F}(\mathrm{F}(1,2), 1)=\mathrm{F}(4,1)=5.$
