Warp paths and alignment

Q. What does the path through the matrix tell us about the correspondence between the test and reference signals?

A. It tells us which samples of the test signal are most similar to the which samples of the reference. It also tells us how much the two signals differ, when best aligned. (This can be derived from the sum of the distances along the warp path.)

A warp path that follows coordinates (1,1), (2,2), (2,3), (3,4), (4,5), (5,6), and (6,7) means:
 

Graphically, this warp path can be portrayed thus:

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