Parsing and Parse Trees$(10\%)$

Suppose that the string abbcabac has the following parse tree $($Figure $1),$ according to some grammar $G.$ List five production rules that must be rules in the grammar $G,$ given that this is a valid parse tree.

Figure $1$: Parse Three

Pushdown Automata$(10\%)$

Consider the following context$-$free grammar G$.$ Construct the Pushdown automata that recognizes $L(G)$

$ETA$

$A+TA$

$A$

$TFB$

$B**FB$

$B$

$F(E)$

$FxF$

$y$

$Fz$