The phrase "after rigorous examination" is correct and usable in written English.
It can be used to indicate that something has been thoroughly analyzed or assessed before reaching a conclusion or decision.
Example: "After rigorous examination of the data, we concluded that the hypothesis was valid."
Alternatives: "following thorough analysis" or "after careful scrutiny".
It will be revised next year after a more rigorous examination.
"So the consideration that I gave in relation to Amir, and it's my discretion so I stand by it and take responsibility for it, was after a very rigorous examination of the entire case, very thorough consideration of his personal reaction – did he plead guilty?
Many of the truly successful innovations were in the judicial system, where the reforming efforts of Samuel von Cocceji resulted in all judges in higher and appellate courts being appointed only after they had passed a rigorous examination.
That is a ramped-up version of normal inspection procedures, and a highly sought-after goal of those who want the plant to undergo the most rigorous examination possible.
The therapeutic efficacy was analyzed by rigorous examination of tumor incidence in the mice 8 weeks after treatment, to evaluate the tumor-free fraction for the different activity concentration levels.
After the ease with which Liverpool, Newcastle and Manchester City sidestepped the potential for embarrassment in the opening games of the Uefa Cup, their credentials are set to be given a more rigorous examination in the second round.
Sarah seems to have got through life without rigorous examination of it.
We look forward to a rigorous examination of the district attorney's evidence".
In a climate of austerity, DfID's commitment to rigorous examination of its performance is important.
The Senate should subject him to a rigorous examination of his priorities before confirming his appointment.
