How do I modify this Levenshtein distance function to work with substrings (Mysql)

I found the function below on the internet that performs check if two words match based on a distance. But the function is no use for me because I need to verify if a substring is contained in a larger string.

   DELIMITER $$
CREATE FUNCTION levenshtein( s1 VARCHAR(255), s2 VARCHAR(255) ) 
  RETURNS INT 
  DETERMINISTIC 
  BEGIN 
    DECLARE s1_len, s2_len, i, j, c, c_temp, cost INT; 
    DECLARE s1_char CHAR; 
    -- max strlen=255 
    DECLARE cv0, cv1 VARBINARY(256); 
    SET s1_len = CHAR_LENGTH(s1), s2_len = CHAR_LENGTH(s2), cv1 = 0x00, j = 1, i = 1, c = 0; 
    IF s1 = s2 THEN 
      RETURN 0; 
    ELSEIF s1_len = 0 THEN 
      RETURN s2_len; 
    ELSEIF s2_len = 0 THEN 
      RETURN s1_len; 
    ELSE 
      WHILE j <= s2_len DO 
        SET cv1 = CONCAT(cv1, UNHEX(HEX(j))), j = j + 1; 
      END WHILE; 
      WHILE i <= s1_len DO 
        SET s1_char = SUBSTRING(s1, i, 1), c = i, cv0 = UNHEX(HEX(i)), j = 1; 
        WHILE j <= s2_len DO 
          SET c = c + 1; 
          IF s1_char = SUBSTRING(s2, j, 1) THEN  
            SET cost = 0; ELSE SET cost = 1; 
          END IF; 
          SET c_temp = CONV(HEX(SUBSTRING(cv1, j, 1)), 16, 10) + cost; 
          IF c > c_temp THEN SET c = c_temp; END IF; 
            SET c_temp = CONV(HEX(SUBSTRING(cv1, j+1, 1)), 16, 10) + 1; 
            IF c > c_temp THEN  
              SET c = c_temp;  
            END IF; 
            SET cv0 = CONCAT(cv0, UNHEX(HEX(c))), j = j + 1; 
        END WHILE; 
        SET cv1 = cv0, i = i + 1; 
      END WHILE; 
    END IF; 
    RETURN c; 
  END$$

This search works, as the distance(difference) between the words doesn't exceeds 4.

     SELECT levenshtein('wooden table', 'woden table')  BETWEEN 0 AND 4 as result FROM test;  

But I needed that something like this also works:

    SELECT levenshtein('woden', 'wooden table')  BETWEEN 0 AND 4 as result FROM test;  

The above search fails because the distance between the words are greater than 4. But if you conside the "substring distance" it matches.