Using Ogden’s Lemma versus regular Pumping Lemma for Context-Free Grammars

Hey guys, so I'm learning the difference between the lemmata in the question. Every reference I can find uses the example:

{(a^i)(b^j)(c^k)(d^l) : i = 0 or j = k = l}


to show the difference between the two. I can find an example using the regular lemma to "disprove" it.

Select w = uvxyz, s.t. |vy| > 0, |vxy| <= p. Suppose w contains an equal number of b's, c's, d's.

I selected:

u,v,x = ε
y = (the string of a's)
z = (the rest of the string w)


Pumping y will just add to the number of a's, and if |b|=|c|=|d| at first, it still will now.

(Similar argument for if w has no a's. Then just pump whatever you want.)

My question is, how does Ogden's lemma change this strategy? What does "marking" do?

Thanks.

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