What is your goal with the commited relationship? If your primary goal is to make that person a part of your life, share life with them, and treat them with respect, love, and honesty, then you are not single! If your goal is to have fun, fullfill needs, and get some laughs than you are not commited, you are single!
Here is the definition of the word commitment :
an agreement or pledge to do something in the future; especially : an engagement to assume a financial obligation at a future date : something pledged : the state or an instance of being obligated or emotionally impelled
“There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results.” - Unknown
“Unless commitment is made, there are only promises and hopes; but no plans.” - Peter F. Drucker