# Is this language is Context-free language or not?

Is anybody can help me please to determine is this language is Context-free language or not?

L={wvw | w,v∈{a,b,c}+}

for example:

part of the language: acbac, abcab, bbcbb

not part of the language: abab, aa, abcc

I tried to prove using pumping lemma for context-free languages like that:

I take this word from language w=aacbbaa. I split the word to 5 parts uvxyz and if I can pump u and y and the word stays inside language the language is context-free:

u-aa, v-cc, x-b, y=bb, z=aa
after I pump v and y the word is still in language->
u-aa, v-cccc, x-b, y=bbbb, z=aa ->
aaccccbbbbbaa


But the answer inside answers section is that the language is not context-free.

What wrong with my prof?

• Same language here: "Is {xyx | |x|≥1} context-free?" cs.stackexchange.com/q/11629/4287, where one of the answers suggests the pumping lemma can be used to show the language is not context-free. – Hendrik Jan Mar 8 '19 at 22:48