Example on match intervals presence at the same time.

interval_matching.sql

-- T_INTERVALS:
--     [-----------------------------[ #1 O
--   08:00                         08:30
--               [---------[ #2 X
--             08:10    08:20
--                                             [-------------------[ #3 O
--                                           08:40               09:00
--                                        [----------[ #4 X
--                                      08:35      08:45
--                                                            [---------[ #5 O 
--                                                          08:55     09:05
--                                                                      [---------[ #6 O
--                                                                    09:05     09:15
--               [---------[ #7 O
--             08:10    08:20
--               [--------------[ #8 X
--             08:10          08:25
--
-- SQL Query: 
--               [--------------[ 
--             08:10          08:25
--                                             [-----[
--                                           08:40 08:45
--

CREATE TABLE
  t_intervals (
    begin_time DATE, 
    end_time DATE, 
    category VARCHAR2(5), 
    code VARCHAR2(5), 
    flag VARCHAR2(1)
  );

INSERT INTO t_intervals(begin_time, end_time, category, code, flag) VALUES (to_date('08:00', 'HH24:MI'), to_date('08:30', 'HH24:MI'), 'A', '#1', 'O');
INSERT INTO t_intervals(begin_time, end_time, category, code, flag) VALUES (to_date('08:10', 'HH24:MI'), to_date('08:20', 'HH24:MI'), 'A', '#2', 'X');
INSERT INTO t_intervals(begin_time, end_time, category, code, flag) VALUES (to_date('08:40', 'HH24:MI'), to_date('09:00', 'HH24:MI'), 'A', '#3', 'O');
INSERT INTO t_intervals(begin_time, end_time, category, code, flag) VALUES (to_date('08:35', 'HH24:MI'), to_date('08:45', 'HH24:MI'), 'A', '#4', 'X');
INSERT INTO t_intervals(begin_time, end_time, category, code, flag) VALUES (to_date('08:55', 'HH24:MI'), to_date('09:05', 'HH24:MI'), 'A', '#5', 'O');
INSERT INTO t_intervals(begin_time, end_time, category, code, flag) VALUES (to_date('09:05', 'HH24:MI'), to_date('09:15', 'HH24:MI'), 'A', '#6', 'O');
INSERT INTO t_intervals(begin_time, end_time, category, code, flag) VALUES (to_date('08:10', 'HH24:MI'), to_date('08:20', 'HH24:MI'), 'A', '#7', 'O');
INSERT INTO t_intervals(begin_time, end_time, category, code, flag) VALUES (to_date('08:10', 'HH24:MI'), to_date('08:25', 'HH24:MI'), 'A', '#8', 'X');
INSERT /*+ APPEND */ INTO t_intervals(begin_time, end_time, category, code, flag) SELECT i.begin_time + 10 / (24 * 60) begin_time, i.end_time + 10 / (24 * 60) end_time, 'B', i.code, i.flag FROM t_intervals i;
COMMIT;

WITH
  joined_intervals
AS (
  SELECT 
    i.category,
    i.flag, 
    MIN(i.begin_time) begin_time,
    MAX(i.end_time) end_time
  FROM
    (
      SELECT
        i.category,
        i.flag, 
        i.begin_time,
        i.end_time,
        MAX(i.group_1) OVER(PARTITION BY i.category, i.flag ORDER BY i.begin_time ASC) group_2
      FROM
        (
          SELECT 
            i.category,
            i.flag, 
            i.begin_time,
            COALESCE(i.end_time, to_date('99991230', 'YYYYMMDD')) end_time,
            CASE
              WHEN 
                    (i.begin_time NOT BETWEEN MIN(i.begin_time) OVER(PARTITION BY i.category, i.flag ORDER BY i.begin_time ASC ROWS BETWEEN UNBOUNDED PRECEDING AND 1 PRECEDING) AND COALESCE(MAX(i.end_time) OVER(PARTITION BY i.category, i.flag ORDER BY i.begin_time ASC ROWS BETWEEN UNBOUNDED PRECEDING AND 1 PRECEDING), to_date('99991230', 'YYYYMMDD')))  
                 OR LAG(i.begin_time) OVER(PARTITION BY i.category, i.flag ORDER BY i.begin_time ASC) IS NULL 
              THEN
                row_number() OVER(PARTITION BY i.category, i.flag ORDER BY i.begin_time ASC)
              ELSE
                -1
            END group_1
          FROM
            t_intervals i
        ) i
    ) i
  GROUP BY
    i.category,
    i.flag, 
    i.group_2
),
  moments
AS (
  SELECT
    m.time, 
    LEAD(m.time, +1) OVER (PARTITION BY m.category ORDER BY m.time) next_time, 
    m.category, 
    m.flag
  FROM
    (
      (
        SELECT
          i.begin_time time, 
          i.category, 
          i.flag
        FROM
          joined_intervals i
      ) UNION (
        SELECT
          i.end_time time, 
          i.category, 
          i.flag
        FROM
          joined_intervals i
      )
    ) m
), 
  split_intervals
AS (
  SELECT
    m.time begin_time, 
    m.next_time end_time, 
    i.category, 
    i.flag
  FROM
    moments m
  JOIN
    joined_intervals i
  ON
      m.category = i.category
  AND i.begin_time <= m.time AND m.time < i.end_time
), 
  match_intervals
AS (
  SELECT
    o.begin_time, 
    o.end_time, 
    o.category
  FROM
    (
      SELECT
        i.*
      FROM
        split_intervals i
      WHERE
        i.flag = 'O'
    ) o
  JOIN
    (
      SELECT
        i.*
      FROM
        split_intervals i
      WHERE
        i.flag = 'X'
    ) x
  ON
        o.begin_time = x.begin_time AND o.end_time = x.end_time
    AND o.category = x.category
)
SELECT
  *
FROM
  match_intervals;
SELECT 
  i.category,
  MIN(i.begin_time) begin_time,
  MAX(i.end_time) end_time
FROM
  (
    SELECT
      i.category,
      i.begin_time,
      i.end_time,
      MAX(i.group_1) OVER(PARTITION BY category ORDER BY i.begin_time ASC) group_2
    FROM
      (
        SELECT 
          i.category,
          i.begin_time,
          COALESCE(i.end_time, to_date('99991230', 'YYYYMMDD')) end_time,
          CASE
            WHEN 
                  (i.begin_time NOT BETWEEN MIN(i.begin_time) OVER(PARTITION BY i.category ORDER BY i.begin_time ASC ROWS BETWEEN UNBOUNDED PRECEDING AND 1 PRECEDING) AND COALESCE(MAX(i.end_time) OVER(PARTITION BY i.category ORDER BY i.begin_time ASC ROWS BETWEEN UNBOUNDED PRECEDING AND 1 PRECEDING), to_date('99991230', 'YYYYMMDD')))  
               OR LAG(i.begin_time) OVER(PARTITION BY i.category ORDER BY i.begin_time ASC) IS NULL 
            THEN
              row_number() OVER(PARTITION BY i.category ORDER BY i.begin_time ASC)
            ELSE
              -1
          END group_1
        FROM
          match_intervals i
      ) i
  ) i
GROUP BY
  i.category,
  i.group_2;

DROP TABLE
  t_intervals;