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Is a^nb^3^n is CsL  or Recursive or Recursive enumerable?

Please draw the state transition diagram also

I think it is not any of them.because b^3^n I can't put in loop
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Is it 3n or 3^n?

If it is 3n then it can be a CFL but if it is 3^n then according to me it should be a Recursive Language.

Please correct me if I am wrong
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It is recursive and i think it's belong to TM as a comparator in which (a<b) condition will satisfy.

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