time complexity(Big-O) of this turing machine

Consider the following language: L = {a^i b^j c^k | i, j, k > 0 and i + j = 2^k}. A TM that decides this language is given below: M = "On input string omega: Scan the input from left to right to determine whether it is a member a^+b^+c^+ of and reject if it is not. Sweep left to right across the tape, crossing off every other a or b. Cross off one symbol c. If after stage 3 the number of a's plus the number of b's is one, and no c. is left, accept. If after stage 3 the number of a a's plus the number of b's is even, and some c's are left on the tape, go to stage 2. Otherwise, reject. " Measure the time complexity of this TM in terms of the length of the input string a^i b^j c^k