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"compound the complexity" is a grammatically correct and usable phrase in written English.
It means to make something more complex or to add to the existing level of complexity. Example: The new system design will compound the complexity of the project, making it more challenging to implement within the given deadline.
Exact(5)
To compound the complexity, the guest chef cannot order ingredients himself.
To compound the complexity, Mr. Shonibare has said that in making the film he was inspired by the current global situation, particularly the war in Iraq.
Furthermore, errors and inconsistency in HIV genotyping compound the complexity in delineating viral mechanisms toward neuropathology.
However these therapies may concern women and compound the complexity of their motherhood decision [ 11].
Patients have depleted bone marrow reserves in the presence of heavily pretreated disease and poor performance status that compound the complexity of the problem.
Similar(55)
Levels of premature cardiovascular death are among the highest in England, almost twice that of the English average, and higher in South Asians for whom type 2 diabetes is a major risk factor for CVD. 15 High turnover of patients, extended overseas visits and changes of address and language compound the complexities of programme delivery.
Because most countries' general aviation rules are far less flexible than America's, expanding Executive Jet's highly complex scheduling system outside the U.S. compounds the complexity.
Compounding the complexity is the fact that the administration is simultaneously asking for a stimulus package of more than $800 billion.
Compounding the complexity of the review was the fact that the agency has never confronted many of the regulatory questions posed by the merger of the two companies.
He had never pressed charges, and the revelations in the paper evoked contradictory feelings, compounding the complexity of issues in the play: matters like sexuality, blame and spirituality.
This compounds the complexity already announced in the July budget to cut income tax relief interest paid for financing such properties".
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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