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これは最も単純なように思えます:
WITH StartTimes AS
(
SELECT DISTINCT username, starttime
FROM dbo.Sessions AS S1
WHERE NOT EXISTS
(SELECT * FROM dbo.Sessions AS S2
WHERE S2.username = S1.username
AND S2.starttime < S1.starttime
AND S2.endtime >= S1.starttime)
),
EndTimes AS
(
SELECT DISTINCT username, endtime
FROM dbo.Sessions AS S1
WHERE NOT EXISTS
(SELECT * FROM dbo.Sessions AS S2
WHERE S2.username = S1.username
AND S2.endtime > S1.endtime
AND S2.starttime <= S1.endtime)
)
SELECT username, starttime,
(SELECT MIN(endtime) FROM EndTimes AS E
WHERE E.username = S.username
AND endtime >= starttime) AS endtime
FROM StartTimes AS S;