We are given the following language B = {$<M,i>$ : M is a turing machine and $i \in \mathcal{N}$ and M accepts some string in atmost $i$ steps }Is language B decidable ?As per a hint from another fellow user, I decided to construct the following decider for B. Call it D.D = On input Enumerate all the strings in $\Sigma^*$ in lexicographical order (shortlex). Let the generated sequence be $s_1,s_2,...$ where each $s_k$ denotes all strings of lenght $k$Simulate each string in $s_k$ on M for atmost i steps. If any of them is accepted, ACCEPT. When we have finished evaluating strings for length $s_i$, output REJECT. Is this the correct decider for B ? 
Is this a correct decider?
undecidability