Solving a recurrence of uneven subproblems without Akra-Bazzi 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.
You could use &quot;guess-and-check&quot;: guess the solution to the recurrence, then use induction to prove that it is a solution, i.e., to prove that your solution satisfies the recurrence.
In your case, since you know Akra-Bazzi, your &quot;guess&quot; can actually be obtained through Akra-Bazzi, but you don't have to tell anyone that's how you obtained your guess.