OK you are right. This counter example is difficult to find. Did you know it before, or you managed to find it so quickly ?

I'm afraid your counter example doesn't work. I have not checked all the axioms (in particular the fact that $d$ is a distance) but the calculus of the last line is wrong. It should be replaced by : $$d(a.x;b.y)+d(a'.x;b'.y) = \frac{3}{2} + \frac{1}{2}+\frac{3}{4} > d((a+a').x;(b+b').y).$$ I'm sorry. Nevertheless, your method for finding a counter example is a good one, I've been looking this way for quite a long without any success.