[danbruc]

Nice puzzle. I found a 18 step solution but of course somebody posted one in the comments years ago.

Why not "one tree can be encoded into seven trees, or one of these 13 remaining cases"?

This direction is no problem, at least if we accept a graph with zero vertices as a tree which is probably non-standard as it should then have -1 edges. But if we allowed it, then a trivial mapping would be T -> (T,Ø,Ø,Ø,Ø,Ø,Ø). The other direction is much more problematic, one can easily map n trees into one, but then one gets stuck with either some trees that do not map back to any tuple or some tuples that have multiple representations. So now I am really curious what makes 7 special, so I will probably have to read the paper after all.