$T(n)=2T(n-1)-1 , for\ n>0$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ , otherwise$
$T(0) = 1$
$T(1) = 2T(0) - 1 = 1$
$T(2) = 2T(1) - 1 = 1$
$T(3) = 2T(2) - 1 = 1$
$T(4) = 2T(3) - 1 = 1$
$...$
So, $T(n) = 1$, for any value of $n$.
i.e. it remains constant.
Time Complexity = O(1)