In class we will see that $!"$ is undecidable, implying that there is

no program to decide if a TM halts on a given input. In this problem we consider the halting

problem for machines with limited memory. Specifically, consider the language:

$=\{<,,>$ : $$ accepts input $$ and never moves its head beyond the first $$ tape cells$\}.$

Is $$ decidable? Explain your answer. $($Hint: what is the outcome when a configuration repeats?$).$