I have a simple recurrence with two variables and cases:
$ f(a,b) = \begin{cases} 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a \leq 0 \\ f(a-1,b)+1~~~~~~ a > b \\ f(a,b-1)+1~~~~~~ otherwise \end{cases} $
I'm trying to use rsolve from Maple but I get nothing.
Here is how I encoded it (very primitive, I agree):
rsolve({f(-abs(a), b) = 0, f(1 + abs(a), abs(a) - abs(b)) = f(abs(a), abs(a) - abs(b))}, f)
Is it possible to solve with Maple? Or any other software??