Turing Machines start with the input string and tape head in the "middle" of a tape that extends infinitely in either direction. Suppose instead that the tape head starts at the "far left" of the tape: the tape extends infinitely to the right, but the tape head can never move further left than its starting position.
This "one-sided Turing Machine" is clearly Turing complete, but I wonder if this new model ever has inferior time complexity to a regular Turing machine.
Are there any languages that require asymptotically more time to decide on a one-sided Turing machine than a regular Turing machine? If so, what is the maximum asymptotic speedup required on a one-sided TM?