Does cost averaging contribute to wash sales?

For example, a stock had a price of $10, and fell to $8 a month later.

I bought 1 stock at $10 on January 1st.

I bought another 1 stock at $8 on February 1st (cost averaging).

 

Then, the stock increased to $9 later.

I sold both stocks at $9 on February 15th.

 

I bought the 2nd stock (the one at $8) less than a month from the time I sold both the stocks. Does this contribute to wash sales?

Thank you!