Let $X$ be a smooth projective curve over an Algebraically closed field $k$. Let $k(X)$ denote its function field.

If $A, B$ are Weil divisors on $X$ such that $A$ is effective (i.e. $A\ge 0$) , then is there any (in)equality between $l(A+B)$ and $ l(B), l(A)$ ?

Here, for a Weil divisor $D$ on $X$, by $l(D)$ we denote the $k$-vector space dimension of the Riemann-Roch space $L(D):=\{f\in k(X)^*: D+ div(f)\ge 0\}\cup \{0\}$.

For a divisor $D$ on $X$, the complete linear system $|D|$ be the collection of all effective divisors which are linearly equivalent with $D$. $|D|$ can be given the structure of a projective space by identifying it with $( L(D)\setminus \{0\})/k^*$ and by that structure, $\dim |D|=l(D)-1$. Now it is known (Hartshorne, Chapter IV, Lemma 5.5) that if $D,E$ are both effective divisors, then $\dim |D|+\dim |E|\le \dim |D+E|$ i.e. $l(D)+l(E)\le l(D+E)+1$ . What I'm basically asking is that if something similar holds if we assume only one of the divisors is effective...