Consistency of shifted exponential estimators

Let $X_1, X_2, \dots, X_n$ be a random sample from a population having the probability density function $$f(x; \mu)=\begin{cases} \frac{1}{2} e^{-\frac{x-2\mu}{2}}, & \text{if }x > 2\mu, \ 0, & \text{otherwise,} \end{cases}$$ where $-\infty < \mu < \infty$. For estimating $\mu$, consider estimators $$T_1 = \frac{\bar{X}-2}{2}\quad\text{and}\quad T_2 = \frac{n X_{(1)}-2}{2n},$$ where $\bar{X}=\frac{1}{n}\sum_{i=1}^n X_i$ and $X_{(1)}=\min\{X_1, X_2, \dots, X_n\}$. Then, which one of the following statements is TRUE?