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Segment Information - Adjusted Operating (Loss) Income (Details) - USD ($)
12 Months Ended
Dec. 31, 2020
Dec. 31, 2019
Dec. 31, 2018
Dec. 31, 2016
Segment Reporting Information [Line Items]        
Operating income $ (988,039,000) $ 363,417,000 $ 562,016,000  
Add back:        
Equity method (loss) income (2,528,000) 2,044,000 2,556,000  
Impairment and related charges 8,684,000 0 0  
Acquisition-related amortization 65,998,000 64,604,000 68,008,000  
Restructuring and other costs 85,797,000 0 0  
Acquisition-related costs 16,787,000 41,037,000 3,266,000  
Litigation costs, net (1,919,000) (24,579,000) 8,323,000  
Stock-based compensation 69,946,000 66,885,000 57,263,000  
Adjusted Operating Income (Loss) (745,274,000) 513,408,000 701,432,000  
Contract cost impairment loss 10,000,000 2,000,000    
Costs to Fulfill Contracts        
Add back:        
Contract cost impairment loss 9,562,000 2,405,000    
Costs to Fulfill Contracts | One Customer        
Add back:        
Contract cost impairment loss 4,000,000      
Hospitality Solutions        
Add back:        
Impairment of intangible assets 5,000,000      
Unasserted Claim        
Add back:        
Litigation accrual 4,000,000   $ 5,000,000  
US Airways Litigation        
Add back:        
Litigation accrual 0     $ 32,000,000
Accrued loss $ (32,000,000) $ (32,000,000)