I am struggling understanding how to apply to pumping lemma to a CF string.
I've got this string:
$$ a^{n}b^{n}c^{m} $$
I would like to understand the steps to apply the pumpuing lemma for this particular string and hence for any other.
At the moment I have tried to decompose the string to $u,v,w,x,y$ with a trial and error approach but I can't figure out what is the procedure to retrive the result systematically.
I know that pumping lemma is condition neccessary but not sufficient to assert that a string belgons to CF, but I would like to understand how to apply the pumpuing lemma to this particular string.
