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Acquisitions (Details)
€ in Billions
 3 Months Ended 12 Months Ended
Oct. 01, 2014
USD ($)
Jan. 07, 2014
USD ($)
brand
continent
Jan. 07, 2014
EUR (€)
Dec. 28, 2013
USD ($)
Dec. 31, 2016
USD ($)
Jan. 02, 2016
USD ($)
Jan. 03, 2015
USD ($)
Jan. 02, 2014
USD ($)
Business Acquisition [Line Items]                
Issuance of common stock         $ 2,805,000 $ 3,670,000 $ 8,612,000  
Goodwill         1,225,893,000 1,233,102,000 1,320,419,000  
Payments to Acquire Businesses, Net of Cash Acquired         8,511,000 377,000 2,094,400,000  
Feed Ingredients [Member]                
Business Acquisition [Line Items]                
Goodwill         797,707,000 796,883,000 847,594,000  
Food Ingredients [Member]                
Business Acquisition [Line Items]                
Goodwill         317,008,000 323,385,000 346,153,000  
Fuel Ingredients [Member]                
Business Acquisition [Line Items]                
Goodwill         $ 111,178,000 112,834,000 126,672,000  
Vion Ingredients [Member]                
Business Acquisition [Line Items]                
Business Combination Provisional Information Initial Accounting Incomplete Adjustment Working Capital             84,000,000  
Business Combination, Consideration Transferred   $ 2,200,000,000 € 1.6          
Foreign Currency Exchange Rate, Translation   1.3605            
Goodwill   $ 702,672,000            
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Inventory   $ 375,306,000            
Business Combination, Goodwill Deductible for Tax Purposes, Percent   33.00%            
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]                
Property plant and equipment   $ 981,009,000            
Deferred tax liability   $ 350,003,000            
Number of Continents in which Entity Operates | continent   5            
Number of Brands Entity Operates | brand   6            
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Cash and Equivalents   $ 91,200,000            
Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Property, Plant, and Equipment             27,300,000  
Business Combination, Provisional Information, Initial Accounting Incomplete, Adjustment, Intangibles             17,600,000  
Business Combination Provisional Information Initial Accounting Incomplete Adjustment Goodwill             72,100,000  
Business Combination Provisional Information Initial Accounting Incomplete Adjustment Other             $ 27,000,000  
Vion Ingredients [Member] | Routes [Member]                
Business Acquisition [Line Items]                
Acquired finite-lived Intangible assets, weighted-average useful life   10 years 10 years          
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]                
Identifiable intangibles   $ 190,200,000            
Vion Ingredients [Member] | Permits [Member]                
Business Acquisition [Line Items]                
Acquired finite-lived Intangible assets, weighted-average useful life   15 years 15 years          
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]                
Identifiable intangibles   $ 225,600,000            
Vion Ingredients [Member] | Patents and Other Intangibles [Member]                
Business Acquisition [Line Items]                
Acquired finite-lived Intangible assets, weighted-average useful life   25 years 25 years          
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]                
Identifiable intangibles   $ 16,500,000            
Vion Ingredients [Member] | Feed Ingredients [Member]                
Business Acquisition [Line Items]                
Goodwill   223,200,000            
Vion Ingredients [Member] | Food Ingredients [Member]                
Business Acquisition [Line Items]                
Goodwill   375,600,000            
Vion Ingredients [Member] | Fuel Ingredients [Member]                
Business Acquisition [Line Items]                
Goodwill   103,800,000            
CustomBlendersCompany [Member]                
Business Acquisition [Line Items]                
Goodwill $ 5,200,000              
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Inventory $ 1,000,000              
Acquired finite-lived Intangible assets, weighted-average useful life 14 years              
Payments to Acquire Businesses, Net of Cash Acquired $ 18,800,000              
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net [Abstract]                
Property plant and equipment 3,200,000              
Identifiable intangibles 8,600,000              
Business Combination, Contingent Consideration, Asset $ 800,000              
Goodwill, Period Increase (Decrease)           $ 500,000    
Common Stock [Member]                
Business Acquisition [Line Items]                
Issuance of common stock       $ 874,000,000        
Senior Notes [Member]                
Business Acquisition [Line Items]                
Face amount of debt insturment               $ 500,000,000
Trademarks and Trade Names [Member] | Vion Ingredients [Member]                
Business Acquisition [Line Items]                
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Indefinite-Lived Intangible Assets   $ 32,000,000