1) Give the definition of “H has β-normal form G”.
2) Recall the lemma which says that if E →β G then E[x := H] →β G[x := H]. Use this lemma and your result above to show that M[x := M] →→β M(MM).
3) Use the above to deduce whether M[x := M] is β-normalising. If yes, give the β-normal form. If the term is not β-normalising, give a detailed proof why it is not.