I am performing a comparison among time series by using Dynamic Time Warping (DTW). However, it is not a real distance, but a distance-like quantity, since it doesn't assure the triangle inequality to hold.

Reminder:`d:MxM->R` is a distance if for all x,y in M:

```
1 - d(x,y) ≥ 0, and d(x,y) = 0 if and only if x = y
2 - It is symmetric: d(x,y) = d(y,x)
3 - Triangle inequality: d(x,z) ≤ d(x,y) + d(y,z)

```

There is any equivalent measure that ensures the condition of *distance* in a matemathical sense? Obviously, I am not looking for a Euclidean distance, but one that ensures the proper classification of my series in a future clustering. 
If so, there is any solid implementation in a R or Python package?