I have written a recurrence relation to describe a recursive algorithm finding the maximum element in an array. The algorthim has an overlap, meaning both of the subarrays that are recurred on contain the middle element of the array.
$T(n) = 2T((n+1)/2) + c$
However, I want to simplify this recurrence relation more.
Since you can often times omit floors and ceilings in recurrence relations, can I omit the $+ 1$?
If so, then my relation is now: $T(n) = 2T(n/2) + c$
Would this alter my big-Theta time complexity? Why or why not?