I believe that sum is actually approximately 2, haha. However, I believe it is implicit that z0 is less than or equal to the maximum of that sum. The maximum can be increased in the algorithm by shifting the starting index, i, to some negative number. If we do iteration i = -2 : inf for instance, the maximum value would be 2^2 + 2^1 + 2^0 + ... = 8.
As for y0 and x0, I suppose the main constraint is that we don't overflow y{ i }, so assuming y0 is positive (similar analysis can include y0 negative): y0 + x0z0 < M -> x0z0 < M - y0 where M is the largest representable number. This is the equation of a hyperbola in x0 and z0, with M - y0 varying linearly in y0. This term represents how much 'room' the other parameters have. If y0 = M, this term is zero indicating we're in big trouble.
Other than overflow, I don't think there are any other constraints, as long as you carry out a large enough number of iterations.