User blog comment:Wythagoras/Friendship function/@comment-1605058-20140717170937/@comment-1605058-20140717192924

Here is an example I meant: http://imgur.com/S0igdSj

If I'm not mistaken, both graphs, while non-isomorphic, have the same friendship function: (q,q)(q,q)(q,q)(q,q)(q,q)(q,q)(q,o)(q,o)(q,o)(q,o)(q,o)(q,o). So the first graph is friendship minor of second and this pair can, for example, be valid sequence for SSCG(11), but not Friend(11).

If we were to operate on friendship functions only, I believe your function is far weaker than you may think. If I'm not mistaken, it doesn't go beyond e_0, possibly not even beyond w^w^w.