Problem 204. yet another flying fly (YAFF)

Same as the previous problem fly fly away but now with two flies! (which of course makes it twice as exciting)

Two flies start always at fixed positions (-100,0) and (100,0), respectively, and they follow two different predefined sequences of discrete jumps (these movements are defined by the vectors dx1 dy1 for the first fly and dx2 dy2 for the second fly). Your job is to determine whether the flies will collide at some point.

The same conditions apply as in the previous problem (100 repetitions of movement sequences maximum). Unscored awesome points if you can find a solution where the algorithm computational time does not increase linearly with the number of repetitions, without requiring the sequences (dx1,dy1) and (dx2,dy2) to be the same size.