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 positive, and replace xi and xi+1 (if exists) by xi - 1 and x1 + ... + xk, respectively. The number of times a vector {n, 0,...0} of length k 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. For example, {2, 0, 0, 0, 0} can be reduced over 2↑‎↑‎21,000,000 times. A Python program for "reducing" vectors is as follows: def max_index(vec):