An undecidable problem on a pair of non-negative integers

For n∈N, f(n) denotes the smallest b∈N such that if a system of equations S⊆{1=x_k, x_i+x_j=x_k, x_i·x_j=x_k: i,j,k∈{0,...,n}} has a solution in N^{n+1}, then S has a solution in {0,...,b}^{n+1}. The author proved earlier that the function f:N→N is computable in the limit and eventually dominates every computable function g:N→N. We present a short program in MuPAD which for n∈N prints the sequence {f_i(n)}_{i=0}^∞ of non-negative integers converging to f(n). Since f is not computable, no algorithm takes as input non-negative integers n and m and decides whether or not ∀(x_0,...,x_n)∈N^{n+1} ∃(y_0,...,y_n) ∈ {0,...,m}^{n+1} (∀k∈{0,...,n} (1=x_k ⇒ 1=y_k)) ∧ (∀i,j,k∈{0,...,n} (x_i+x_j=x_k ⇒ y_i+y_j=y_k)) ∧ (∀i,j,k∈{0,...,n} (x_i \cdot x_j=x_k ⇒ y_i \cdot y_j=y_k)).