I don't follow you there:

The path becomes ["EAST", "WEST"], now "EAST" and "WEST" annihilate each other...

Going in one direction and immediatly going in the opposite one should be avoided.

@Chrono79, as you said ["NORTH", "WEST", "SOUTH", "EAST"] is not reducible, am agree

but how's ["EAST", "WEST"] not the same as the example above?? it's reducible too, isn't it?! why is [] acceptable not ["EAST", "WEST"] as it is?

[north, south, west, east] is [], but the first statement is of course, wrong.

No, they're not, and order matters in a path. Anyone that worked with a map would know that.

correct, they are same, order is not important. anyone worked with vectors would know that

[north, west] and [west,north] are the same thing

No, they're not. The paths are different, and there are rules about how to reduce the path, so:

The result of [north, south, west, east] should be []

Yes, but ["NORTH", "WEST", "SOUTH", "EAST"] is not reducible. And it's shown in the description.