Use the general algorithm to transform the following pushdown automaton into a context-free grammar. this automaton has 4 states: the starting state s, the reading state r, the checking state c, and the final state f. the transitions are as follows: from s to r, the transition is: ε, ε → $; from r to r, the transitions are: a, ε → a; b, ε → b; from r to c, we have a jump ε, ε → ε. from c to c, the transitions are: a, a → ε b, b → ε from c to f, the only transition is: ε, $ → ε. show, step-by-step, how the resulting grammar will generate the sequence abba.