The part of the sentence 'complicated by the notion that' is correct and usable in written English.
This phrase generally precedes an idea, opinion, or concept that complicates an existing situation. For example: The decision-making process was complicated by the notion that the only viable solution would require financial investments beyond our current budget.
Not only does he long to leave his job -- a notion complicated by the fact that this would mean leaving his partner, who is also his father (Mr. Sutherland) -- but he has also become obsessed with an outspoken, provocative young woman, played by Neve Campbell, whose presence disturbs Alex's compartmentalized suburban world, where he lives with his wife (Tracey Ullman) and young son (David Dorfman).
(As noted in Olsson, 2005, section 3.5, the matter is somewhat complicated by the fact that Lewis adopted a notion of independence that is weaker than Conditional Independence. Ironically, Lewis's weaker notion turns out to be compatible with the combination of Nonfoundationalism and Coherence Justification).
And things are made more complicated by the fact that, during his exposition, Heidegger freely employs a number of closely related notions, including 'assignment', 'indication' and 'reference'reference
Although apparently consistent with the notion that onset learning is encoded by different timing mechanisms to those involved in offset judgments, this idea is complicated by the finding that auditory offset learning does transfer to onset tasks [46].
The hunt is further complicated by the fact that prices can swing widely by neighborhood.
The situation is further complicated by the fact that all of these studies have flaws.
Mr. Creighton's job is complicated by the fact that the unions often take differing positions.
And it is now complicated by the fact that the real economy is slowing".
This is further complicated by the fact that the feed is always refreshing.
The Ségolène problem is complicated by the fact that it is not just political but personal.
