On sets of generators of $l$-ary semigroup $\langle A^k,[\,\,]_{l,\sigma,k}\rangle$

The problem of finding, from a known generating set of the semigroup $A$, the generating set of the $l$-ary semigroup $\langle A^k,[\,\,]_{l,\sigma,k}\rangle$ with the $l$-ary operation $[\,\,]_{l,\sigma,k}$, which is defined on the $k$-th Cartesian power of an arbitrary groupoid $A$ for any integer $l\ge2$ and any permutation $\sigma$ from the set $\mathbf{S}_k$ of all permutations of the set $\{1, 2,\dots,k\}$ has been solved.