How do you prove that a set is not freely generated?

Question

Let's say we define the set of “babble-strings” inductively as follows:

• “ba” is a babble-string;
• if s is a babble-string, so is “ab”⌢s;
• if s and t are babble-strings, so is s⌢t

Let us call this set C. How would one prove that C is not freely generated?

Thanks!