  Symmetry of information states that $C(x) + C(y|x) = C(x,y) + O(\log C(x))$.
We show that a similar relation for online Kolmogorov complexity does not hold.
Let the even (online Kolmogorov) complexity of an n-bitstring $x_1x_2... x_n$
be the length of a shortest program that computes $x_2$ on input $x_1$,
computes $x_4$ on input $x_1x_2x_3$, etc; and similar for odd complexity. We
show that for all n there exist an n-bit x such that both odd and even
complexity are almost as large as the Kolmogorov complexity of the whole
string. Moreover, flipping odd and even bits to obtain a sequence
$x_2x_1x_4x_3\ldots$, decreases the sum of odd and even complexity to $C(x)$.
