  We establish a coding theorem and a matching converse theorem for separate
encodings and joint decoding of individual sequences using finite-state
machines. The achievable rate region is characterized in terms of the
Lempel-Ziv (LZ) complexities, the conditional LZ complexities and the joint LZ
complexity of the two source sequences. An important feature that is needed to
this end, which may be interesting on its own right, is a certain asymptotic
form of a chain rule for LZ complexities, which we establish in this work. The
main emphasis in the achievability scheme is on the universal decoder and its
properties. We then show that the achievable rate region is universally
attainable by a modified version of Draper's universal incremental Slepian-Wolf
(SW) coding scheme, provided that there exists a low-rate reliable feedback
link.
