HELP!!! Big-O of my anagram program

This is probably a very stupid question. I made a working program that reads in a word list and spits out all the anagram classes in the word list in alphabetical order. For example, if the program read in the list:

car
dog
bed
stop
god
pots
arc
tops

the program will output:

arc car
bed
dog god
pots stop tops

If you're familiar with coding anagram programs, I used two sorts:

- Quicksort to sort out the individual words. The original and the sorted words are stored in each node of the link list.
- Mergesort to sort out the linked list.

My questions are, what would be the Big-O running time of my program if the input word list have N words and L is the maximum length of any word? (would it be NlogN+LlogL since the two sorts have a Big-O of nlogn?)

Also, what would be the Big-O if the input list contains only two words?

I'm not familiar with anagram programming, but it seems that the growth rate would be NlogN. It wouldnt be NlogN + LlogL becuase when you determine the growth rate of a function, you only count the fastest growing term. Growth rate is similar to the degree of a polynomial, the degree just determines how fast the values will grow. Since the polynomial

x^4 + x^3 + x^2 + x

has a degree of 4, it follows that the growth rate of a function would be determined by the fastest growing portion of your algorithm.

>x^4 + x^3 + x^2 + x

yes, monomials of higher terms make those of lower terms negligible in their scale, regardless of whether they are exponential or logarithmic...