It's not going to affect the integrity of the program, but this is rather amusing:
const int led1 = 10; // led output pin
const int led2 = 11; // led output pin
const int led3 = 13; // led on arduino board
...
digitalWrite(led1, LOW); //stop second led
digitalWrite(led2, HIGH); //start third led
led1 is the second led and led2 is the third led. So what is led1? This is probably an example of comments confusing rather than helping.