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Is the halting problem decidable for TMs that do not write to the tape?

Once a read only tape TM repeats a configuration, it will loop forever. Therefore, all we have to do to decide the above is construct a different TM(with read and write tape) that’s takes the read only TM as input and checks for a repeat configuration, if one is found, accept, otherwise reject.

Is this correct?

JMF9
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