I think you need a couple of extra variables. One which tells the current number of words in the array, and another which tells you whether there is a duplicate. I also changed the printf format to %s.
/* check array with strcmp */
//num_of_words is the current number of words in the array
duplicate = false;
for (array_counter=0; array_counter<num_of_words; array_counter++)
if (strcmp(user, words[array_counter]) == 0)
printf("DUPLICATE \"%s\"", user);
duplicate = true;