The ET-trees will store the ET-sequences as $(a,b)$-trees with the parameter~$a$ set upon
initialization of the structure and with $b=2a$. We know from the standard theorems of $(a,b)$-trees
(see for example \cite{clrs}) that the depth of a~tree with $n$~leaves is always $\O(\log_a n)$
and that all basic operations including insertion, deletion, search, splitting and joining the trees
run in time $\O(b\log_a n)$ in the worst case.
The ET-trees will store the ET-sequences as $(a,b)$-trees with the parameter~$a$ set upon
initialization of the structure and with $b=2a$. We know from the standard theorems of $(a,b)$-trees
(see for example \cite{clrs}) that the depth of a~tree with $n$~leaves is always $\O(\log_a n)$
and that all basic operations including insertion, deletion, search, splitting and joining the trees
run in time $\O(b\log_a n)$ in the worst case.