Transformation monoid minimisation

For every $n \in \mathbb{N}$, the full transformation monoid $T_n$ is the set of (total) functions from $\{1,2,\ldots,n\}$ to $\{1,2,\ldots,n\}$, equipped with the standard function composition. The symmetric group $S_n$ is the subroup of $T_n$ composed of all the permutations. What is the complexity of the following decision problems with respect to the parameter $n$: Problem 1: Given a submonoid $\langle s_1,s_2\rangle \subseteq T_n$ generated by two elements, does there exist an integer $m$ smaller than $n$ such that $\langle s_1,s_2\rangle$ can be embedded in $T_m$? Problem 2: Given a subgroup $\langle g_1,g_2\rangle \subseteq S_n$ generated by two elements, does there exist an integer $m$ smaller than $n$ such that $\langle g_1,g_2\rangle$ can be embedded in $S_m$?