I encountered the following recurrence relation in homework, for which we need to find its asymptotics: $$T\left(n\right)=T\left( \frac{n}{3} \right) + T\left( \frac{n}{6} \right) + 1$$
I observed it is possible to approach this relation with the method of Akra-Bazzi, however this method was not taught in class. Akra-Bazzi gives the result of $\theta(n^p)$ where $p$ is the unique solution to $$\frac{1}{3^p}+\frac{1}{6^p}=1$$
However, since this was not taught, I would like to ask if there's a different method to tackle this exercise, or a way to find its asymptotics more constructively.