  Let $F$ be the category with the set of objects $\bf N$ and morphisms being
the functions between the standard finite sets of the corresponding
cardinalities. Let $Jf:F\rightarrow Sets$ be the obvious functor from this
category to the category of sets. In this paper we construct, for any relative
monad $\bf RR$ on $Jf$ and a left module $\bf LM$ over $\bf RR$, a C-system
$C({\bf RR},{\bf LM})$ and explicitly compute the action of the B-system
operations on its B-sets.
  In the following paper it is used to provide a rigorous mathematical approach
to the construction of the C-systems underlying the term models of a wide class
of dependent type theories.
  This paper is a result of evolution of arXiv:1407.3394. However this paper is
much more detailed and contains a lot of material that is not contained in
arXiv:1407.3394. It also does not cover some material that is covered in
arXiv:1407.3394.
