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The word 'rigorous' is correct and commonly used in written English
It means thorough, strict, and demanding a high level of accuracy or attention. You can use 'rigorous' in situations where something requires careful and precise examination, testing, or analysis. It can also be used to describe a challenging or demanding task or activity. Example: The research project had to undergo rigorous testing and peer review before being published in a scientific journal. Example: The rigorous selection process for the job required several rounds of interviews and assessments. Example: The training program was designed to be rigorous in order to prepare athletes for the challenges of the competition.
Dictionary
rigourous
adjective
Nonstandard spelling of rigorous
Exact(12)
They often sit on company boards, where their input is welcomed as practical, relevant and rigourous.
Steyn was an injury doubt for the first Test having spent seven weeks on the sidelines with a groin strain and, although he passed a rigourous fitness test before Christmas, South Africa believe the lay-off may have been a contributing factor to his current problems.
Dozens of other organisations have undergone his rigourous and humane scrutiny since then: Kansas City PD (Law And Order, 1969), the US Marine Corps boot camp at Fort Knox (Basic Training, 1971), the vivisection industry (Primate, 1974), the Racetrack (1985).
Notably, they are demanding Athens "undertake rigourous reviews and modernisation" of collective bargaining and industrial action.
When is the FSA going to give up its absurd quest to create the most complicated and rigourous form of new regulation and start, instead, implementing the existing measures?
New regulations requiring rigourous checks on refrigeration towers were reported to be going to the cabinet today.
Phillip Darnton, who was chair of Cycling England and is now chief executive of Bicycle Association, welcomed the new study: "This is an extremely rigourous and robust analysis of available data.
Two older composers they made an exception for; one was Anton Webern, whose rigourous form of serialism was to be an inspiration for them; he, however, was already dead, killed accidentally by a member of the occupying forces in Vienna.
Ramesh dismissed it, saying it was "not a product of rigourous scientific evaluation".
Blunkett was grudging, saying the reforms were "not as bad as some feared" before questioning Gove over examination details, while Abbott was more effusive in agreeing for the need for "rigourous" qualifications.
Rigourous rules govern such exchange (prohibiting "bargaining in bad faith" and so on), but they are different rules than those that govern a dialogue which functions as a search for truth.
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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