We employ the model-theoretic method of Ehrenfeucht-Fraisse games to p
rove the completeness of the theory CFT, which has been introduced by
G. Smolka and R. Treinen (1994, J, Logic Programming 18(3), 229-258) f
or describing rational trees in a language of selector functions. The
comparison to other techniques used in this field shows that Ehrenfeuc
ht-Fraisse Games lead to simpler proofs, (C) 1998 Academic Press.