In such a compressed ternary search tree, the number of nodes is less than twice the number of strings--for each string there is at most one new node added and one existing node split into two nodes.
The number of nodes is less than twice the number of strings. This is in such a compressed ternary search tree. There is at most one new node added. This was for each string. There is at most one existing node split into two nodes. This was for each string.