I want to find the worst-case running time of an algorithm, which follows the following recurrence equation: The worst-case running time is $\Theta(n^2) + T(n, 2, n)$, where
$T(x, i, y) = \begin{cases} 1 & \textrm{if $(x=0)$ or $(y=0)$ or $(i > n)$} \\ x+y+ T(x-a,\quad i+1, \qquad b)\\ \ \qquad+ T(x-a,\quad i+1,\ y-b)\\ \ \qquad+ T(\quad\ \ \ a,\quad i+1,\ y-b) & \textrm{otherwise} \end{cases}$
where $a \in \{0, ..., x\}, b \in \{0, ..., y\}$, and $a,b$ can be different in each recursion step, dependent on the input.
(Note: $x$ and $y$ represent the sizes of two lists $|L_1|=x, |L_2|=y$, and in each recursion step, each list is split into two, i.e. into lists of size $a$ and $x-a$ (for $L_1$), and $b$ and $y-b$ respectively (for $L_2$).)
How can I analyze such a recurrence equation, i.e. determine $f$ s.t. $T(n, 2, n)\in O(f)$? In particular, I do not know how to deal with $a, b$, especially since they are completely dependent on the input of the algorithm.
(I can solve the recurrence equation for special cases of $a,b$, e.g. $a=\frac{x}{2}, b=\frac{y}{2}$ for all recursion steps, or $a=x, b=0$ for all recursion steps etc., but not in general.)