---------- Backtracking search for Theorem 1(b) ----------

There are only finitely many 10/3-free words with at most 5 palindromes avoiding all factors in []. The longest such word has length 70.


---------- Backtracking search for Theorem 1(c) ----------

There are only finitely many 2/1-free words with at most 15 palindromes avoiding all factors in []. The longest such word has length 42.


---------- Backtracking search for Theorem 1(d) ----------

There are only finitely many 41/22-free words with at most 17 palindromes avoiding all factors in []. The longest such word has length 449.


---------- Check of short cube-free binary words for Theorem 3(a) ----------

The f-image of every binary cube-free word y of length at most 24 is 10/3-plus-free.


---------- Backtracking search for Theorem 5 ----------

There are only finitely many 9/4-free words with at most 6 palindromes avoiding all factors in ['11', '22']. The longest such word has length 18.


---------- Check of short binary 7/3-plus-powers for Theorem 5 ----------

For every binary word w with exponent greater than 7/3 and period less than 18, the word obtained from w by adding a 2 in the middle of every factor 10 contains a factor of exponent greater than 9/4.


---------- Backtracking search for Theorem 8(c) ----------

There are only finitely many 25/13-free words with at most 17 palindromes avoiding all factors in ['010']. The longest such word has length 131.


---------- Backtracking search for (a) => (b) in Lemma 15 ----------

There are only finitely many 2/1-free words with at most 16 palindromes avoiding all factors in ['010']. The longest such word has length 60.