Please explain query intervals output

I found this query on older thread and i can not uderstand output interval
pairs:

How to find min and max values in date intervals:
--------------------------------------------------
Input:
CREATE TABLE INTERVALS
(key CHAR(5) NOT NULL
,level CHAR(7) NOT NULL
,date_from DATE NOT NULL
,date_to DATE NOT NULL
);

INSERT INTO INTERVALS
VALUES
('key1', 'level1', '2001-05-01', '2002-10-01')
,('key1', 'level1', '2001-01-01', '2001-04-30')
,('key1', 'level1', '2000-11-10', '2000-12-31')
,('key1', 'level1', '2000-06-01', '2000-10-09')
,('key1', 'level1', '2000-01-01', '2000-05-31')
;

SELECT l.key, l.level, l.date_from, r.date_to
FROM Intervals l
Intervals r,
WHERE NOT EXISTS
(SELECT *
FROM Intervals le
WHERE le.date_to = l.date_from - 1 DAY)
AND r.date_to =
(SELECT MIN(date_to)
FROM Intervals rm
WHERE rm.date_to > l.date_from
AND NOT EXISTS
(SELECT *
FROM Intervals re
WHERE re.date_from = rm.date_to + 1 DAY));

or

SELECT l.key, l.level, l.date_from
, (SELECT MIN(date_to)
FROM Intervals rm
WHERE rm.date_to > l.date_from
AND NOT EXISTS
(SELECT *
FROM Intervals re
WHERE re.date_from = rm.date_to + 1 DAY)
) AS date_to
FROM Intervals l
WHERE NOT EXISTS
(SELECT *
FROM Intervals le
WHERE le.date_to = l.date_from - 1 DAY);

Same output:

KEY LEVEL DATE_FROM DATE_TO
----- ------- ---------- ----------
key1 level1 2000-11-10 2002-10-01
key1 level1 2000-01-01 2000-10-09

2 record(s) selected.
What is the meaning of this output;
The min value in intervals are
2001-01-01
The max value in intervals are
2002-10-01
Please help
Thank's

--
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On 3 Okt, 14:42, "lenygold via DBMonster.com" <u41482@uwe> wrote:
[...]
>
> INSERT INTO INTERVALS
> VALUES
>  ('key1', 'level1', '2001-05-01', '2002-10-01')
> ,('key1', 'level1', '2001-01-01', '2001-04-30')
> ,('key1', 'level1', '2000-11-10', '2000-12-31')
> ,('key1', 'level1', '2000-06-01', '2000-10-09')
> ,('key1', 'level1', '2000-01-01', '2000-05-31')
> ;
>
[...]

> KEY   LEVEL   DATE_FROM  DATE_TO    
> ----- ------- ---------- ----------
> key1  level1  2000-11-10 2002-10-01
> key1  level1  2000-01-01 2000-10-09
>
>  2 record(s) selected.
> What is the meaning of this output;
> The min value in intervals are
> 2001-01-01
> The max value in intervals are
> 2002-10-01
> Please help
> Thank's
>

Not sure what you find confusing, but I think it will become clear to
you if you draw a timeline from '2000-01-01' to '2002-10-01' and then
put the intervals in the input ontop of that:

00-01-01..00-05-31
00-06-01..00-10-09
<--
> 00-11-10..00-12-31

01-01-01..

/Lennart