theory of computation

Question

L = { <M,w> / M is a TM,w is a string and M on simulating w,the Read/write head of M moves 100 steps away from the left most symbol of input }.Assume initially the Read/write head is in left-most symbol of input. 

MY ANSWER : This language is Recursively enumerable but not recursive ...right ??? 

Comments

It should be recursive. The question is basically restricting the tape size to 100 elements which is a finite number. With finite space in the input tape, a TM cannot do infinite moves unless it is repeating the same stuff which can be detected.

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@arjun sir , if it is repeating the same stuff how it can be detected ?

Answer 1

L = { <M,w> / M is a TM,w is a string and M on simulating w,the Read/write head of M moves 100 steps away from the left most symbol of input }.Assume initially the Read/write head is in left-most symbol of input.

i think it should be regular language because the number of steps are finite and countable which is in the case of the regular language.