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We respectfully reply to Wang et al.'s reply to our comment to their [JHEP$\textbf{09}$ (2021) 053]. Some more subtleties and details are discussed forhopefully better clarification and understanding, especially about theconditions in Hilbert's finiteness theorem. We also disprove Wang et al.'sincorrect assertion in their reply [arXiv:2110.13865 [hep-ph]] that there is anisomorphism between ${\rm U}(n,\mathbb{C})$ and ${\rm GL}(n,\mathbb{C})$. Wegive two proofs for our argument. One proof is in the context of Lie group forarbitrary positive integer $n$, and the other proof is in the context ofabstract group for $n=3$ which can also be generalized to $n\geq 3$. In orderto better illustrate the intrinsic differences between a compact Lie group andits complexification, we choose ${\rm SU}(n,\mathbb{C})$ and ${\rmSL}(n,\mathbb{C})$ as a pair of examples and give two proofs for the generallynon-isomorphic relation between them. One proof is in the context of Lie groupfor integers $n\geq 2$, and the other proof is in the context of abstract groupfor $n=3$ which can again be generalized to $n\geq 3$.

(Reply to)$^{\textbf{2}}$ "Comment on 'Flavor invariants and  renormalization-group equations in the leptonic sector with massive Majorana  neutrinos' "