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 L1={wlwRw∈{a,b}∗,l∈{a,b} }

which type of language is this DCFL or NDCFL? (note that l∈{a,b} not {a,b}*)

I feel its NDCFL can you also tell how PDA will look like?

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Yeah this is not only DCFL but also regular. So, FSA is enough. It has to accept the regex of the form 

a(a+b)*a+b(a+b)*b + a + b

edited by
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no it will be ncfl ryt? . because for w supppose it will be  aaab than l can be any (a+b) so here we can't do the work determiniatically so it will be cfl but not dcfl

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