The question requests to find the recurrence relation of the following algorithm and solve it using the characteristic equation.
\begin{align} &\text{SORT}(A[0\dots n-1])\colon\\ &\quad \text{if } n = 2 \text{ and } A[0] > A[1] \text{ then} \\ &\quad\quad \text{swap}(A[0],A[1]) \\ &\quad \text{else if } n > 2 \text{ then} \\ &\quad\quad m=\lceil 2n/3 \rceil \\ &\quad\quad \text{SORT}(A[0\dots m-1]) \\ &\quad\quad \text{SORT}(A[n-m\dots n-1]) \\ &\quad\quad \text{SORT}(A[0\dots m-1]) \end{align}
The recurrence equation that I found is $T(n) = 2 \cdot T(2n/3) + T(n/3) + 1$ with base case $T(2) = 5$.
The base case is $T(2) = 5$ because of 2 comparisons in the if statement plus 3 statements in swap() function.
I'm not sure whether what I've tried is correct or not. All help is appreciated!