December 31,
2019
2018
2017
Gross unrecognized tax benefits at beginning of year
$490
$220
$293
Increases in tax positions for prior years
7,718
36
—
Increases in tax positions for current year
1,839
320
32
Decreases in tax positions for prior years
(412)
—
—
Lapse in statute of limitations
—
(86)
(105)
Gross unrecognized tax benefits at end of year
$9,635
$490
$220

text: A reconciliation of the beginning and ending balances of the total amounts of gross unrecognized tax benefits is as follows (in thousands):
text: The total liability for gross unrecognized tax benefits as of December 31, 2019, 2018 and 2017 includes $9.6 million, $0.4 million and $0.2 million, respectively, of unrecognized net tax benefits which, if ultimately recognized, would reduce our annual effective tax rate in a future period. These liabilities, along with liabilities for interest and penalties, are included in accounts payable and accrued expenses and Other long-term liabilities in our consolidated balance sheet. Interest, which is included in Interest expense in our consolidated statement of income, was not material for all years presented.
text: During the year ended December 31, 2019, we recognized an increase in unrecognized tax benefits of approximately $7.7 million related to an increase in research and development tax credits available to us for tax years 2016-2018 and $1.8 million for the 2019 tax year.
text: We are subject to income taxes in the U.S., various state and foreign jurisdictions. Tax statutes and regulations within each jurisdiction are subject to interpretation and require significant judgment to apply. We are no longer subject to U.S. federal or non-U.S. income tax examinations by tax authorities for the years before 2015. We are no longer subject to U.S. state tax examinations by tax authorities for the years before 2014. We believe it is reasonably possible that within the next year our unrecognized tax benefits may decrease by $1.9 million due to the acceptance of a portion of our amended research and development credits.

Questions:
question: What does the table show us?
answer: A reconciliation of the beginning and ending balances of the total amounts of gross unrecognized tax benefits
question: The company believes that it is possible that within the next year, unrecognized tax benefits may decrease by $1.9 million. What causes that decrease?
answer: the acceptance of a portion of our amended research and development credits
question: What did the increase of approximately $7.7 million in unrecognized tax benefits relate to, during the year ended December 21, 2019?
answer: an increase in research and development tax credits available to us for tax years 2016-2018 and $1.8 million for the 2019 tax year.
question: What is the percentage change of gross unrecognized tax benefits from the end of the year 2017 to 2018?
answer: 122.73
derivation: ($490-$220)/$220 
scale: percent
question: What is the proportion of the total increase in tax positions for the prior and current years over gross unrecognized tax benefits at the end of the year 2019?
answer: 0.99
derivation: (7,718+1,839)/9,635
question: What is the total lapse in the statute of limitations from 2017 to 2019?
answer: -191
derivation: -105+(-86)+0
scale: thousand