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Let En = {xk = 1, xi + xj = xk, xi &#x00B7; xj = xk : i, j, k &#x2208; {1, ..., n}}. For a positive integer n, let f (n) denote the smallest non-negative integer b such that for each system S &#x2286; En with a solution in non-negative integers x1, ..., xn there exists a solution of S in non-negative integers not greater than b. We prove that if a function &#x0393; : &#x2115; \ {0} &#x2192; &#x2115; is computable, then f dominates &#x0393; i.e. there exists a positive integer m such that &#x0393;(n) &lt;; f (n) for any n &#x2265; m. For positive integers n, m, let g(n,m) denote the smallest non-negative integer b such that for each system S &#x2286; En with a solution in {0, ..., m - 1}n there exists a solution of S in {0, ..., b}n. Then, equations and equation We present an infinite loop in MuPAD which takes as input a positive integer n and returns g(n,m) on the m-th iteration.

MuPAD codes which implement limit-computable functions that cannot be bounded by any computable function