Problem #WSP-000029

Problem

There is a triangle with side lengths $a$, $b$ and $c$. Does there exist a triangle with side lengths $|a-b|$, $|b-c|$ and $|c-a|$? Does it depend on what $a$, $b$ and $c$ are?
Recall that a triangle can be formed with side lengths $x$, $y$ and $z$ if and only if all the inequalities $x+y>z$, $y+z>x$ and $z+x>y$ hold.