Why does decimation make a system time variant? On Wikipedia I read this : "The Discrete Wavelet Transform, often used in modern signal processing, is time variant because it makes use of the decimation operation."

Why does decimation makes system time variant?
HINT:
Think about the following situation: you have an input signal with alternating ones and zeros, and you decimate by a factor of $2$. Now shift the input signal by one sample and compute a new output signal by decimating by a factor of $2$. Is the output signal a shifted version of the previous output signal? If the system is time-invariant, shifting the input signal causes the output signal to shift by the same amount.