It's possible that the 'to' path and the 'from' path have not a single
point in common (except for the starting and ending points, of course).
Thus klakla may be false only because the paths don't cross/overlap, and
not because the goer didn't go from x2 to x3 and then from x3 to x2.
Similarly for x5. I postulate that x4 and x5 be thrown away. (There's
another possibility: dump two new places for the returning path, i.e. "x1
goes from x2 to x3, first going via x4 by x5, then returning via x6 by x7".
Good luck using that.)