`LinkedHashSet`, for the intents and purposes of being accessed using `contains` is simply a hash set.  It uses the return from `hashCode` of the objects inserted in it to determine the position to place it in in the hash set.  If you have a collision, then it will then check the next element.  If that is occupied, it will then check the one after that, and so forth.  Therefore, for hash sets with relatively small capacity or types which do not return distinguishable `hashCode` values, you will see up to `O(n)` complexity for insertion or checking the esistence of an item in the hash set.  However most times you don't see collisions and so in most cases it will be `O(1)`.

Combine this with a `O(n)` operation on all entires in your `ArrayList`, and you end up with `O(n)*O(1)` complexity on average or `O(n)`.  However if the `hashCode()` does not properly distinguish values or if the capacity is small for the `LinkedHashSet`, you may see up to `O(n*m)` complexity (`O(n)*O(m)`) where n is the number of elements in your `ArrayList` and m being the number of elements on average in each `LinkedHashSet`.

Hope that answers your question!