Alternate Sample Variance III

Let $X_1,\dots, X_n \sim N(\mu,\sigma^2)$ IID. Define

$$V = \dfrac{1}{2(n-1)}\sum_{i=1}^{n-1} (X_{i+1} - X_i)^2$$

Find the efficiency of $V$ relative to $s^2$ as $n \rightarrow \infty$, where $s^{2}$ is the typical expression for sample variance.

NOTE: It is highly recommended to complete Alternate Sample Variance I, Alternate Sample Variance II, and Sample Variance Variance before attempting this question.