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RIR stands for Reduction in Recruitment. This process will be acceptable when companies have been advertising to recruit for open positions for a while and have not been able to fill the positions.
This process is used in lieu of the labor ceritifcation process which will include placing an ad in the paper and waiting for the responses from american citizens. This process is set up to protect american workers prior to sponsoring a foreign national.
Not all companies can apply for RIR. The company should prove that they have been trying to hire in the past 6 months atleast and the positions have not been filled. RIR cases used to a cake walk in the last 2-3 years given the economy and the boom in the job market. With the changed scenario, I think the DOL will look into the RIR cases more carefully.
You can get more info on these issues at severel web sites such as imminfo.com, immigration.com, etc.,
Hope this helps