CN-LEAGUE 2005 Problem 2

Assume that positive numbers $a, b, c, x, y, z$ satisfy $cy + bz = a$ , $az + cx = b$ , and $bx + ay = c$ . Find the minimum value of the function $$f(x, y, z) = \frac{x^2}{x+1} + \frac {y^2}{y+1} + \frac{z^2}{z+1}.$$