The starting point of Dynamic Time Warping

Consider there are 2 real-time time series. And they didn't start at the same time. Say, time-series $s_1$ is from $t_1$ to $t_n$ and time-series from $t_2$ to $t_m$. And $t_1$ is not equal to $t_2$.

I didn't see any assumption of DTW so I guess it is still applicable to this situation with some necessary modification. So, all in all, how can we calculate the distance using DTW between 2 time series if their starting points are not the same?