Is it true that groups $< a,b| a^n b^k=b^ka^{n+1}, b^la^s=a^sb^{l+1}\>$ are non-trivial for almost all (in any sense:))) $n,k,l,s\in\mathbb N$?

Is it true that groups $\langle a,b \mid a^n b^k=b^ka^{n+1}, b^la^s=a^sb^{l+1}\rangle$ are non-trivial for almost all (in any sense:))) $n,k,l,s\in\mathbb N$?