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Identify the type of the given language and draw the corresponding automata for the language.

$L=\left \{a^{i}b^{j}c^{k} \space\ | \space\ j=max(i,k) \right \}$

A] Regular
B] DCFL
C] CFL but not DCFL
D] Non-CFL

answer given is option D
Not sure where exactly I am going wrong but I was thinking the given language as $L=\left \{a^{i}b^{j}c^{k} \space\ | \space\ j=i \space\ or \space\ j=k \right \}$

Could you please correct why it is wrong to think like this.

assume I=2, k=3

now j=2 according to your language bt wrt qsn it should be 3(max)

@ankitgupta.1729 can u prove this language non-cfl by other methods apart from pumping lemma ?