Metric non-invariant under permutation of the coordinates

Question

I need to prove that in $\mathbb C^2$ the function $d:\mathbb C^2 × \mathbb C^2 → [0, \infty)$ defined by

$$d(x,y)=|x_1 −y_1|+|x_1 −y_1 −x_2 +y_2|$$

is a metric that is not invariant under permutation of the coordinates.

I have tried to give a counterexample, for example:

Let $x$, $y$ $\in \mathbb C^2$ then compute their distance $d(x,y)$, after that permutate the coordinates of the vectors, getting $x'$, $y'$ and recalculate the distance $d(x',y')$, but the distances that I obtained are the same (which I don't want, I need them to be different).