So I have to check if $Y_t$ is Wiener process first:
$$\operatorname{E}[Y_t]=0$$
$$\operatorname{Cov}(Y_s,Y_t)=\min\{s,t\}$$
First condition is easy, but with the second i came across the problem: $$ \operatorname{Cov}(Y_s,Y_t)=\operatorname{E}[Y_sY_t] = \operatorname{E}\left[ (s+1) X_{\frac{s}{s+1}}(t+1) X_{\frac{t}{t+1}} \right] = (t+1)(s+1) \operatorname{E} \left[X_{\frac{t}{t+1}}X_{\frac{s}{s+1}}\right]$$
If $X_t$ is Brownian motion then $E[X_sX_t]=\min\{s,t\}$? But if i suppose that, for example, $s<t$, then second condition is false cause I end with something like $(t+1)s$.
What am I doing wrong?