... eventually the initial path of lengthN of Ck, then eventually the initial path of length N of Akis the initial path of length N of BC. Eventually, the terminal path of length N of Akis the terminal ... sequence of pathsin G, then either {Ak} is constant or, for all N, the initial and terminal paths of Ak of length N are eventually constant.Proof. The proof is by induction on the complexity of ... isconstant, then eventually the terminal path of length N of Akis the terminalpath of length N of a concatenation of B’s. If {Bk} is not constant, theneventually the terminal path of length N of...