While exhaustive search guarantees finding the optimal sequence, it incurs a prohibitive computational cost of $\mathcal{O}(|\mathcal{Y}|^{T'})$, where $|\mathcal{Y}|$ is the vocabulary size and $T'$ is the sequence length. This exponential growth makes it practically infeasible; for instance, evaluating a sequence of length $T'=10$ with a vocabulary of $|\mathcal{Y}|=10000$ would require assessing $10000^{10} = 10^{40}$ sequences, which is beyond the capabilities of foreseeable computers.