Let L_{3} = {a^{i}bc^{j} | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L_{3}. Use the construction of the proof to extend the automaton to one that recognizes L_{3}. Give a path through your extended automaton corresponding to a string in L*_{3}. and show how the argument of the proof splits it into paths through your original automaton.