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Income Taxes - Unrecognized Tax Benefits Reconciliation, Table (Details) - USD ($) $ in Millions | 12 Months Ended
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Jan. 31, 2020 | Jan. 31, 2019 | Jan. 31, 2018
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward] |  |  |
Gross unrecognized tax benefits at the beginning of the fiscal year | $ 209.0 | $ 337.6 | $ 261.4
Increases for tax positions of prior years | 2.8 | 7.9 | 22.8
Decreases for tax positions of prior years | (0.4) | (146.3) | (22.5)
Increases for tax positions related to the current year | 11.1 | 10.3 | 78.4
Decreases relating to settlements with taxing authorities | 0.0 | 0.0 | (0.8)
Reductions as a result of lapse of the statute of limitations | (1.9) | (0.5) | (1.7)
Gross unrecognized tax benefits at the end of the fiscal year | $ 220.6 | $ 209.0 | $ 337.6

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