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The phrase "acknowledge the complication of" is correct and usable in written English.
You can use it when discussing a complex issue or situation that requires recognition of its intricacies.
Example: "In our analysis, we must acknowledge the complication of the various factors influencing the outcome."
Alternatives: "recognize the complexity of" or "accept the intricacies of".
Exact(1)
He did acknowledge the complication of allowing married priests into the church.
Similar(59)
Sejal Worah, the programme director of the World Wide Fund for Nature (WWF) in India, said that Greenpeace is effective at pulling issues into public attention, but that it does not acknowledge the complications of what people want.
We acknowledge the complications of these backcrossing experiments and have therefore removed them from the final version of the manuscript.
Mr. Bloom acknowledges the complications of fraud and practicality, but says he's sure that the government, if it really wants to, can find adequate safeguards.
Mr. Kaishian acknowledged the complications of standardized testing including what he called the "high-stake nature of testing that can be inherently unfair," confined as it is to only a snapshot of a student at any given moment and that may not convey the quality of any one school.
Baggini acknowledges the complication that religious believers might operate with different readings of the term supernatural, but then brushes this aside as secondary.
On "Death or Glory", Strummer examines his life in retrospect and acknowledges the complications and responsibilities of adulthood.
While acknowledging the complications posed by the recent massacre of 16 Afghans, apparently by a lone American soldier, and the loss of 6 British soldiers to a roadside bomb, Mr. Obama and Mr. Cameron insisted that the American-led coalition was making gains in preparing Afghans to take over their own security.
The question is whether acknowledging the complications requires serious revision or even rejection of the central claim.
The younger Mr. Woodman acknowledged the complications.
The new business plan acknowledges the complications involved in crossing the mountains.
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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