I want to draw the following figure without pstricks:

What I have is the following code:
\documentclass{minimal}
\usepackage{forest}
\usepackage[external]{adjustbox}
\newcommand{\menge}[1]{%
\mbox{%
$%
\left\{%
\ignorespaces#1%
\right\}%
$%
%\\[-1.5mm]
}%
}
\forestset{
tag/.style={for tree={parent anchor=south, child anchor=north,align=center,base=top}},
% a style that creates an arrow pointing to the substitution node from a tree top node encoded as daughter
substitution/.style={edge={<-,dashed},l+=\baselineskip}}
\begin{document}
\menge{
\adjustbox{valign=c}{%
\begin{forest}
tag
[S
[NP$_1^1\downarrow$]
[S,name=s1]]
\end{forest}
}
\hspace{1cm}
\adjustbox{valign=c}{%
\begin{forest}
tag
[S,name=s2
[NP$_1^1$
[e]]
[VP
[NP$_1^2\downarrow$]
[S*]
[V$_1$
[versprach]]]]
%\draw(s1.south)--(s2.north);
\end{forest}
}
}
\end{document}
I think connecting two nodes would be the logically correct way to do this, but the scope of the node naming ends with the forest environment, doesn't it. Is there another way to do this?
minimalfor examples. As has been pointed out before, it is not appropriate for this purpose. – cfr Oct 16 '14 at 23:09