  Vine copulas are a flexible way for modeling dependences using only
pair-copulas as building blocks. However if the number of variables grows the
problem gets fast intractable. For dealing with this problem Brechmann at al.
proposed the truncated R-vine copulas. The truncated R-vine copula has the very
useful property that it can be constructed by using only pair-wise copulas, and
conditional pair-wise copulas. In our earlier papers we introduced the concept
of cherry-tree copulas. In this paper we characterize the relation between the
cherry-tree copulas and the truncated R-vine copulas. Both are based on
exploiting of some conditional independences between the variables. We give a
necessary and sufficient condition for a cherry-tree copula to be a truncated
R-vine copula. We introduce a new perspective for truncated R-vine modeling.
The new idea is finding first a good fitting cherry-tree copula of order $k$.
Then, if this is also a truncated R-vine copula we apply the Backward Algorithm
introduced in this paper. This way the construction of a sequence of trees
which leads to it becomes possible. So the cherry-tree copula can be expressed
by pair-copulas and conditional pair-copulas. In the case when the fitted $k$
order cherry-tree copula is not a truncated R-vine copula we give an algorithm
to transform it into truncated R-vine copula at level $k+1$. Therefore this
cherry-tree copula can also be expressed by pair-copulas.
