Background: the page Graphic lambda calculus.
Let be a graph in with one input and one output. For any graph with one output, we denote by the graph obtained by grafting the output of to the input of .
Problem: Given , find such that , where means any finite sequence of moves in graphic lambda calculus.
The solution is in principle the same as in usual lambda calculus, can you recognize it? Here is it. We start from the following:
That’s almost done. It suffices to do this:
to get a good graph :