How to determine the complexity of a Turing machine from its state table?

I have an algorithm that is implemented by the following state table for a Turing machine:

I want to determine the algorithm's complexity. To do that I think I should count the number of steps the Turing Machine makes before halting.

But I don't know the input on the tape.

How can I determine the complexity of this algorithm without knowing the input?

Assuming the start state is 𝑞₁, the TM head will move to the right side of the input and then transition to state 𝑞₂. Now realise that whatever happens after this point, the TM will never get back to state 𝑞₁ again. Also, the only head-moves that can happen from this point onwards are 𝐿 (left), whether the state is 𝑞₂ or 𝑞₃, with one exception when the blank at the left side of the input is reached in state 𝑞₂: then an 𝑆 (no move) can occur exactly once and then the state transitions to 𝑞₀, which is an end-state (as there are no transitions defined for 𝑞₀).

The head first moves to the extreme right and then back to the extreme left; the number of executed transitions is thus near 2𝑛 (to be precise: 2𝑛+2), where 𝑛 is the size of the input, and so we can say the complexity is O(𝑛).

If we analyse more closely, we can see that this algorithm takes a binary representation of an integer and increments it by one. It does so by flipping all right-sided 1 to 0 and the 0 that delimits that suffix (or if none is present: a blank) is flipped to a 1.

To test the TM a bit, you can use the implementation below:

createTuring({
    transitions: [
        { state: "q1", read: "01",            move: "R", nextState: "q1" },
        { state: "q1", read: "_",             move: "L", nextState: "q2" },
        { state: "q2", read: "0", write: "1", move: "L", nextState: "q3" },
        { state: "q2", read: "1", write: "0", move: "L", nextState: "q2" },
        { state: "q2", read: "_", write: "1",            nextState: "q0" },
        { state: "q3", read: "01",            move: "L", nextState: "q3" },
        { state: "q3", read: "_",             move: "R", nextState: "q0" },
    ],
    initState: "q1",
    tape: "11101101",
});

<script src="https://trincot.github.io/turing.js"></script>