# Can the halting problem for bounded Turing machines be efficiently decided?

A Turing machine is given. The following problem is decidable :

Does the Turing-machine stay within given bounds of the tape (for example in the range $-100$ to $100$) AND halt ?

The problem is decidable because eventually the Turing machine must repeat an earlier configuration (and then never halts) or halt or leave the given range. My question :

Is there an efficient method to decide this variant of the halting problem ? Or do we have to let the machine run and note the configurations until we recognize a repetition or the machine halts ?

The good news is that you can calculate how many possible configurations there are and at least get some upper bound as to how many steps you may have to run the machine so you don't go in blind ... though that upper bound will quickly become too large for practical purposes, e.g. with the tape going out 100 squares to the left and right and assuming a binary alphabet you already have $2^{201}$ possible tape-configurations and thus even more state-tape configurations .. not good!