Oracle 18c

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CREATE TABLE a AS
SELECT 123 AS ID, 'abc' AS VAL
FROM DUAL;
1 rows affected

CREATE TABLE b AS
SELECT *
FROM a;
1 rows affected

CREATE OR REPLACE TRIGGER trg_1 AFTER UPDATE ON a FOR EACH ROW WHEN (new.val<>old.val)
BEGIN
  UPDATE b
  SET b.val = :new.val
  WHERE b.id = :new.id;
END trg_1;
/
CREATE OR REPLACE TRIGGER trg_2 AFTER UPDATE on b FOR EACH ROW WHEN (new.val<>old.val)
BEGIN
  UPDATE a
  SET a.val = :new.val
  WHERE a.id = :new.id;
END trg_2;
/
UPDATE a
SET a.val = 'def'
WHERE a.id = 123;
ORA-04091: table FIDDLE_JYRHVLBZCPEPHSLWHQVV.A is mutating, trigger/function may not see it
ORA-06512: at "FIDDLE_JYRHVLBZCPEPHSLWHQVV.TRG_2", line 2
ORA-04088: error during execution of trigger 'FIDDLE_JYRHVLBZCPEPHSLWHQVV.TRG_2'
ORA-06512: at "FIDDLE_JYRHVLBZCPEPHSLWHQVV.TRG_1", line 2
ORA-04088: error during execution of trigger 'FIDDLE_JYRHVLBZCPEPHSLWHQVV.TRG_1'

CREATE OR REPLACE PACKAGE pk_trigger_chk IS
  suppress BOOLEAN := FALSE;
END pk_trigger_chk;
/
CREATE OR REPLACE TRIGGER trg_1 AFTER UPDATE ON a FOR EACH ROW WHEN (new.val<>old.val)
BEGIN
  IF NOT(pk_trigger_chk.suppress) THEN
    pk_trigger_chk.suppress := TRUE;
    
    UPDATE b
    SET b.val = :new.val
    WHERE b.id = :new.id;
    
    pk_trigger_chk.suppress := FALSE;
 END IF;
EXCEPTION WHEN OTHERS THEN
  pk_trigger_chk.suppress := FALSE;
END trg_1;
/
CREATE OR REPLACE TRIGGER trg_2 AFTER UPDATE ON b FOR EACH ROW WHEN (new.val<>old.val)
BEGIN
  IF NOT(pk_trigger_chk.suppress) THEN
    pk_trigger_chk.suppress := TRUE;
    
    UPDATE a
    SET a.val = :new.val
    WHERE a.id = :new.id;
    
    pk_trigger_chk.suppress := FALSE;
 END IF;
EXCEPTION WHEN OTHERS THEN
  pk_trigger_chk.suppress := FALSE;
END trg_2;
/
UPDATE a
SET a.val = 'def'
WHERE a.id = 123;
1 rows affected

SELECT 'A' AS TABLE_NAME, a.id, a.val
FROM a
UNION ALL
SELECT 'B', b.id, b.val
FROM b;


TABLE_NAME
ID
VAL


A
123
def

B
123
def