Self doubt

Question

L = { a$^{m}$b$^{n}$ /  m < n , m>=0 , n>=1 }

Is the language DCFL or CFL ?

Comments

I think it's deterministic context-free language.

1.take stack push all the a's in the stack.

2. here according to condition there will be at least one b.For every b pop a's from the stack the here will

3 conditions.

case1:  a's are greater than b's.

case2: a's and b's are equal.

case3: a's are less than b's

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Yes it should be $DCFL$

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If the processing symbol is 'b' then there can be two operations in q0

1. Either to pop 'a'

2. No operation as w = bbbb can be a possible input

So still will it be deterministic?