Friedman's vector reduction problem

The vector reduction problem is a combinatorial problem researched by Harvey Friedman.

Let x = {x1...xk}. Find the greatest i < k such that xi is non-negative, and replace x and xi+1 by xi - 1 and xi + ... + xk, respectively.

The number of times a vector {n, 0,...0} can be reduced is lower bounded by A(k - 1, b) and upper bounded by A(k + 1, n + c), where A is Friedman's version of the Ackermann function and c is a constant.