System Optimization Gains, Net (Losses) Gains, Net (Details) $ in Thousands	3 Months Ended					12 Months Ended
	Jan. 01, 2017 USD ($)	Oct. 02, 2016 USD ($)	Apr. 03, 2016 USD ($)	Jan. 03, 2016 USD ($)	Jun. 28, 2015 USD ($)	Jan. 01, 2017 USD ($) Restaurant	Jan. 03, 2016 USD ($) Restaurant	Dec. 28, 2014 USD ($) Restaurant	Dec. 29, 2013 Restaurant	Feb. 28, 2015 Restaurant
Property, Plant and Equipment [Line Items]
Significant Changes, Planned Franchises to Sell | Restaurant										540
Future company-owned restaurant ownership percentage										5.00%
System optimization gains, net
Significant Changes, Franchises Sold | Restaurant								255
Proceeds from sales						$ 262,173	$ 204,388	$ 161,386
System optimization gains, net	$ 23,825	$ 37,756	$ 8,426	$ 59,258	$ 15,654	71,931	74,009	91,510
Goodwill	$ 741,410			770,781		$ 741,410	$ 770,781	$ 822,562
Sale of Company-Owned Restaurants to Franchisees [Member]
System optimization gains, net
Significant Changes, Franchises Sold | Restaurant						310	327	237	244
Proceeds from sales						$ 251,446	$ 193,860	$ 128,292
Net assets sold						(115,052)	(86,493)	(53,043)
Goodwill related to sales of restaurants						(41,561)	(29,970)	(18,032)
Net (unfavorable) favorable leases						(24,592)	(846)	34,335
Other						(3,103)	(5,499)	(5,692)
Gain on sales of restaurants, Net, Before post-closing adjustments						67,138	71,052	85,860
Post-closing adjustments on sales of restaurants						(1,411)	1,285	(1,280)
System optimization gains, net						65,727	72,337	84,580
Favorable Lease Assets						7,612	34,437	63,120
Unfavorable Lease Liabilities						$ 32,204	35,283	$ 28,785
Deferred Gain on Sale of Property				$ 4,568			$ 4,568
Franchises Sold, Deferred Gain on Sale | Restaurant							17
Recognition of Gain on Sale of Property							$ 4,492
Sale of franchise-operated restaurant to franchisee [Member]
System optimization gains, net
Significant Changes, Franchises Sold | Restaurant						144	71	18
Proceeds from sales								$ 15,779
System optimization gains, net								1,841
Goodwill								0
Sale of Other Assets [Member]
System optimization gains, net
Proceeds from sales						$ 10,727	$ 10,478	17,263
System optimization gains, net						6,204	1,672	5,089
Sale of company-owned restaurants and other assets [Member]
System optimization gains, net
System optimization gains, net						$ 71,931	74,009	89,669
Guarantee Obligations [Member] | Sale of Company-Owned Restaurants to Franchisees [Member]
System optimization gains, net
Deferred Gain on Sale of Property								$ 1,995
Franchises Sold, Deferred Gain on Sale | Restaurant								8
Canada, Dollars | Guarantee Obligations [Member] | Sale of Company-Owned Restaurants to Franchisees [Member]
System optimization gains, net
Deferred Gain on Sale of Property								$ 2,300
System Optimization [Member]
System optimization gains, net
Goodwill, Transfers							$ 11,429	$ 8,457