Fixed points in graphic lambda calculus

Background: the page Graphic lambda calculus.

Let A be a graph in GRAPH with one input and one output. For any  graph B with one output, we denote by A(B) the graph obtained  by grafting the output of B to the input of A.

Problem:  Given A, find B such that A(B) \leftrightarrow B, where \leftrightarrow 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 B:



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