Adjust edge endpoints depending on node label

Question

I would like to draw a tree where the position of edge endpoints relative to the node depends on contents of the node, and may change between the parent edge and the child edges, to point out a relationship between the two labels. Here is an example of what I want to draw:

Note that the child edges of the middle node are positioned differently from that of its own child edges. (Fortunately, I can assume that all of a node's child edges should be positioned at the same position: it is the case in this example, but it would not be the case if, e.g., the middle node "S(b, c)" had a child "V(b, f)".

Is there a clean way to draw this kind of tree?

Edit: My current approach is to use tikz-qtree:

\documentclass[tikz,border=5pt]{standalone}
\usepackage{tikz-qtree}
\begin{document}
\begin{tikzpicture}
\Tree
[.{$R(a, b)$}
  [.{$S(b, c)$}
    [.{$T(c, d)$} ]
    [.{$U(e, c)$} ]
  ]
];
\end{tikzpicture}
\end{document}

With the expected result:

The problem is that the tree edges do not represent clearly the common elements from one node label to the other. Sadly I do not have much experience with Tikz or qtree so I don't have a specific idea of how to improve this...

Answer 1

This uses forest and it takes significant amounts of manual intervention to work. However, it is the best I can come up with right now. (I don't know tikz-qtree at all and I could not see any way to achieve this from the documentation. qtree might be a possibility as it allows you to execute TeX code using ! but then you would lose the power of TiKZ within the tree itself.)

\documentclass[border=5pt, tikz, mult]{standalone}
\usepackage{forest}
\begin{document}

  \begin{forest}
    for tree={
      inner sep=1pt
    }
    [{$R(a, b)$}, parent anchor=-35, anchor=-35
      [{$S(b, c)$}, parent anchor=-40
        [{$T(c, d)$}, child anchor=90
        ]
        [{$U(e, c)$}, child anchor=45
        ]
      ]
    ]
  \end{forest}

\end{document}