# Does forcing TMs to change all symbols they read change their power?

If we limit a turing machine so that it is not allowed to write the symbol that it reads would it reduce its power?

For example: $( State, A, State, Z, DIRECTION)$

$A$ cannot be the same symbol as $Z$.

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I'll take the original alphabet and double it -- so for symbol $a$, I create two symbols $a_1$ and $a_2$, and for symbol $b$, I create $b_1$ and $b_2$.
Now I treat both $a_1$ and $a_2$ in the exact same way as the old TM treated $a$, except when I'm supposed to write an $a$ back onto an $a$, I check if the current symbol is $a_1$ or $a_2$ and write the other one.