User blog comment:Wythagoras/Friendship function/@comment-5529393-20140718081359/@comment-1605058-20140718121536

This is exactly the problem I had with the use of Higman's lemma you mentioned. If we change definition of friendship minor so that _some_ reordering of brackets has to satisfy the inequalities, then indeed we can use that, but otherwise infinite antichains arise, just like in your example.