Is it possible to reduce the complexity of radix-2 FFT if the input vector contains identical elements? my question is about reducing the complexity of radix-2 FFT when the input vector has a specific structure.

For an input vector of x with N elements, the complexity is given by O(N log2 N).

My input vector y with N elements has the structure of:
y = [x1 x2]T

where,

x1 = x2

and x1 and x2 vectors have N/2 elements. Is it possible to reduce the complexity of radix-2 FFT for this y vector? I think it is possible to not use one of the N/2 DFT blocks of the FFT algorithm in this case. Can anyone show me what is the complexity for this vector? Thanks in advance.
if

$$\text{FFT}\{[a, b, c, d]\} = [p, q, r, s]$$

then

$$\text{FFT}\{[a, b, c, d, a, b, c, d]\} = [p, 0, q, 0, r, 0, s, 0]$$

or 
$$=[2p, 0, 2q, 0, 2r, 0, 2s, 0]\text,$$

depending on normalization.

Edit:
Using this property, we can make FFT nearly 2x faster on this specialized data. But the complexity is still $O(n \log n)$. I mean, big O notation doesn't count constant factor.