Complex sentence: Later on the size of Czechoslovak contingent became significantly smaller, and, after the peaceful split of Czechoslovakia, and after both new republics agreed on the fact that the Czech Republic would take over its membership in the NNSC.
Split into simpler sentences: Later on the size of Czechoslovak contingent became significantly smaller. After the peaceful split of Czechoslovakia, both new republics agreed that the Czech Republic would take over its membership in the NNSC.