What is the grammar for language $L = \{ a^nb^m : n\neq m-1\}$?

I only know I have to write grammar for both $ n<m-1 $ and $ n>m-1 $, so this is what I wrote:

for n<m-1
S->Abb
A->aAb|lambda

for n>m-1
S->aaA
A->aAb|lambda

Yet I can not mix them and get a correct grammer for it.

What is the grammar for language $L = \{ a^nb^m : n\neq m-1\}$?

I only know I have to write grammar for both $ n<m-1 $ and $ n>m-1 $, so this is what I wrote:

• For $n<m-1$: \begin{align} &S\to Abb \\ &A\to aAb \mid \lambda \end{align}

• For $n>m-1$: \begin{align} &S\to aaA \\ &A\to aAb \mid \lambda \end{align}

Yet I can not mix them and get a correct grammar for $L$.

What is the grammar for language $L = \{ a^nb^m : n!=m-1\}$?

I only know I have to write grammar for both $ n<m-1 $ and $ n>m-1 $, so this is what I wrote:

for n<m-1
S->Abb
A->aAb|landa

for n>m-1
S->aaA
A->aAb|landa

Yet I can not mix them and get a correct grammer for it.

What is the grammar for language $L = \{ a^nb^m : n\neq m-1\}$?

I only know I have to write grammar for both $ n<m-1 $ and $ n>m-1 $, so this is what I wrote:

for n<m-1
S->Abb
A->aAb|lambda

for n>m-1
S->aaA
A->aAb|lambda

Yet I can not mix them and get a correct grammer for it.