For the given deterministic pushdown automata shown in Fig. 4, would it accept the language {aⁿb²ⁿ | n >= 0} by final state? Use the execution of the string a²b⁴ to justify your answer.

-or hop pop b, a pop- 2 Start X nop b, a nop pop nop a, a push(a) push(a) Fig. 4