Turing Machine for the Language L = a^n b^n | Automata Theory

Start at the beginning of the input tape.
Scan the tape from left to right, looking for the first "a". If no "a" is found, accept the input and halt. Otherwise, move the head to the right of the "a".
Scan the tape from the current position to the right, looking for the first "b". If no "b" is found, reject the input and halt. Otherwise, move the head to the right of the "b".
Scan the tape from the current position to the left, looking for the first "a". If no "a" is found, reject the input and halt. Otherwise, move the head to the left of the "a".
Repeat steps 3-4 until there are no more "a"s or "b"s to the right or left of the current head position.
If the tape is now blank, accept the input and halt. Otherwise, reject the input and halt.
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