Can Recurrence Relations with Complex Inequalities Be Simplified?

[seeker101]

Any suggestions on how to approach solving:

$$\Psi(m,n) \leq \Psi\left(\left \lfloor\frac{m}{2}\right\rfloor,n_1\right) + \Psi\left(\left \lceil\frac{m}{2}\right\rceil,n_2\right) + 16n^*+11m \lceil\text{log }m\rceil$$

where $$n = n_1 + n_2 + n^*$$

 

[JSuarez]

I would start by making m = 2^k. This would give you a more simple recursion, but that inequality and the arbitrary partition of n makes me wonder if it's possible to go beyond a partial computational solution.