"complicated rule" is correct and usable in written English.
You can use it to refer to a complex set of instructions or a regulation that is hard to understand or follow. For example, "We must abide by the complicated rule that specifies how things must be done."
One of the paradoxes of Mr. Putin's long, complicated rule is that when he came to power at the end of 1999, television — a little like the country — was worn down and uninspired, a limp blend of telenovelas and knockoffs of American and European shows.
This complicated rule has several parts governing sampling (e.g., mandating "first draw" sampling for residences), monitoring strategy, and the prescribed response, which includes public education, notification of responsible officials, measures to reduce personal and family exposure, and initiation of a program to replace lead service lines on public property.
Most modern machines have complicated rule sets, and learning what those rules are is a major part of getting high scores.
The agency uses complicated rules to settle which beneficiaries receive how much additional coverage.
Buying a home overseas requires navigating what are often complicated rules on foreign ownership.
It has been known as an audit trap, in part because complicated rules have resulted in filing errors.
At the time, chip designs followed complicated rules and were painstakingly patterned by hand on Mylar sheets.
Because more government breeds complicated rules and laws that a small business can't afford to follow.
The key to games education is to start with a simple game and add increasingly complicated rules.
Outside contractors provide cancer treatment; to get it patients may have to navigate complicated rules and restrictions.
The outrage grew as the new media further scrutinized the caucus process, and many Maine officials became embarrassed at the Byzantine nature and the party's complicated rules.
