Shareholders' Equity - Shareholders' Equity Activity (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended						9 Months Ended
	Sep. 30, 2024	Jun. 30, 2024	Mar. 31, 2024	Sep. 30, 2023	Jun. 30, 2023	Mar. 31, 2023	Sep. 30, 2024	Sep. 30, 2023	Dec. 31, 2023
Schedule of Issued and Treasury Shares [Line Items]
Ordinary Shares, Issued (in shares)	72,700,000						72,700,000		72,100,000
Ordinary Shares, Outstanding (in shares)	72,700,000						72,700,000		72,100,000
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Balance, beginning balance	$ 1,240	$ 1,100	$ 922	$ 672	$ 586	$ 551	$ 922	$ 551
Net Income	166	137	123	131	90	81	426	302
Equity Awards, Granted, Vested and Exercised, Net of Shares Withheld for Taxes	9	12	4	9	6	(43)
Share Repurchases	(50)						(50)
Dividends Declared	(19)
Other Comprehensive Loss	20		(24)	(35)	(10)	3
Equity Issued for Acquisitions			75
Distributions to Noncontrolling Interests	(10)	(9)		(15)		(6)
Other				1
Balance, ending balance	$ 1,356	1,240	1,100	763	672	586	$ 1,356	763
Dividend declared (in dollars per share)	$ 0.25
Acquisitions
Schedule of Issued and Treasury Shares [Line Items]
Ordinary shares issued for acquisition (in shares)							844,702
Capital in Excess of Par Value
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Balance, beginning balance	$ 2,997	2,985	2,906	2,891	2,885	2,928	$ 2,906	2,928
Equity Awards, Granted, Vested and Exercised, Net of Shares Withheld for Taxes	9	12	4	9	6	(43)
Share Repurchases	(50)
Equity Issued for Acquisitions			75
Balance, ending balance	2,956	2,997	2,985	2,900	2,891	2,885	2,956	2,900
Retained Income (Deficit)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Balance, beginning balance	(1,717)	(1,842)	(1,954)	(2,217)	(2,299)	(2,371)	(1,954)	(2,371)
Net Income	157	125	112	123	82	72
Dividends Declared	(19)
Balance, ending balance	(1,579)	(1,717)	(1,842)	(2,094)	(2,217)	(2,299)	(1,579)	(2,094)
Accumulated Other Comprehensive Income (Loss)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Balance, beginning balance	(52)	(52)	(28)	(29)	(19)	(22)	(28)	(22)
Other Comprehensive Loss	20		(24)	(35)	(10)	3
Balance, ending balance	(32)	(52)	(52)	(64)	(29)	(19)	(32)	(64)
Noncontrolling Interests
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Balance, beginning balance	12	9	(2)	27	19	16	(2)	16
Net Income	9	12	11	8	8	9
Distributions to Noncontrolling Interests	(10)	(9)		(15)		(6)
Other				1
Balance, ending balance	$ 11	$ 12	$ 9	$ 21	$ 27	$ 19	$ 11	$ 21