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The phrase "a complicated system" is correct and usable in written English.
It can be used when describing a system that has many interconnected parts or is difficult to understand.
Example: "The new software operates on a complicated system that requires extensive training to navigate effectively."
Alternatives: "a complex system" or "an intricate system".
Exact(60)
Voting is a complicated system.
It's a complicated system and can be confusing to navigate.
They also set up a complicated system of consultation.
The economy is a complicated system, with many moving parts.
You can achieve full visibility of a complicated system but not of a complex one.
A receiver is a complicated system consisting of RF, analog and mixed-signal components.
In the male cells, the activists negotiated a complicated system of competing interests.
They set up a complicated system of communicating through a shared Gmail account.
Member states' approval is determined through a complicated system of a majority based largely on population.
The mayor of Paris is elected through a complicated system, something like America's electoral college.
"This is a complicated system that has existed for 10 years.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com