What could be the loop invariant for the following algorithm (addition of natural numbers)

Question

I'm trying to prove the correctness of the following function and I'm having trouble determining the loop invariant:

function add(y, z) //returns y + z

x = 0; c = 0; d = 1;
while (y > 0) or (z > 0) or (c > 0) do

a = y % 2;
b = z % 2;
if a xor b xor c then x = x + d;
c = (a and b) or (b and c) or (a and c);
d = 2d; y = ⌊y/2⌋; z = ⌊z/2⌋;

return(x)

On my own, I thought (a and b = c) is the loop invariant, because it was true for every iteration in the set of values of y and z that I've tested. I'm not really sure how that factoid is relevant in proving the correctness of the algorithm.