I have a question about a specific pumping lemma problem for Context-Free Languages.
Suppose we have the following Language:
L = {(a^i)(b^j)(c^k)(d^l) | 0 < i < k AND j > l > 0 }
Here is my attemp to prove that the language is not context-free:
Assume L context-free. Take the constant n>0 from the lemma.
Let Z = (a^n)(b^n+1)(c^n+1)(d^n), Z ∈ L.
Than according to the lemma, Z can be written as Z = uvwxy where the following properties hold:
1. |vx| >= 1
2. |vwx| <= n
3. for every i >= 0, u(v^i)w(x^i)y ∈ L.
We have 6 different possibilities for vwx
1. vwx = a^i, i <= n
2. vwx = (a^i)(b^j), i+j <= n
3. vwx = b^i, i <= n
4. vwx = (b^î)(c^j), i+j <= n
5. vwx = (c^i), i <= n
6. vwx = (c^i)(d^j)), i+j <= n
Is this right so far ? The things that I'm unsure off, is if my different cases of vwx is right.
Thanks in advance
