UPDATE + JOIN + TRIGGERS = table doesn't exists error

CREATE TABLE `a` (`id` INT NOT NULL, `x` INT NOT NULL DEFAULT 1, PRIMARY KEY (`id`));

CREATE TABLE `b` (`id` INT NOT NULL, `x` INT NOT NULL DEFAULT 1, PRIMARY KEY (`id`));

CREATE TABLE `c` (`id` INT NOT NULL, `x` INT NOT NULL DEFAULT 1, PRIMARY KEY (`id`));

CREATE TABLE `d` (`id` INT NOT NULL, `x` INT NOT NULL DEFAULT 1, PRIMARY KEY (`id`));

INSERT INTO `a` (`id`, `x`) VALUES ('1', '1');

INSERT INTO `b` (`id`, `x`) VALUES ('1', '1');

INSERT INTO `c` (`id`, `x`) VALUES ('1', '1');

INSERT INTO `d` (`id`, `x`) VALUES ('1', '1');

DELIMITER $$

CREATE DEFINER = CURRENT_USER TRIGGER `a_AFTER_UPDATE` AFTER UPDATE ON `a` FOR EACH ROW

BEGIN

    UPDATE c SET c.x = c.x + NEW.x-OLD.x WHERE c.id=NEW.id;

END$$

CREATE DEFINER = CURRENT_USER TRIGGER `c_BEFORE_UPDATE` BEFORE UPDATE ON `c` FOR EACH ROW

BEGIN

DECLARE y INT;

    SET y = (SELECT x FROM d WHERE d.id=NEW.id);

    SET NEW.x = NEW.x + y;

END$$

DELIMITER ;

UPDATE a JOIN b ON a.id=b.id SET a.x=a.x+b.x WHERE a.id=1;