A commutator bound - siddhartha-gadgil/Superficial GitHub Wiki

Gross proof time

Here is a computer generated proof of a bound on the length of the commutator aba̅b̅ for a linear norm on the free group with the lengths of the generators bounded above by 1.

1. • |a̅| ≤ 1.0
2. • |b̅a̅b| ≤ 1.0 using |a̅| ≤ 1.0
3. • |b̅| ≤ 1.0
4. • |ab̅a̅| ≤ 1.0 using |b̅| ≤ 1.0
5. • |a̅b̅aba̅b̅| ≤ 2.0 using |a̅b̅a| ≤ 1.0 and |ba̅b̅| ≤ 1.0
6. • |a| ≤ 1.0
7. • |bab̅| ≤ 1.0 using |a| ≤ 1.0
8. • |b| ≤ 1.0
9. • |a̅ba| ≤ 1.0 using |b| ≤ 1.0
10. • |aba̅b̅ab| ≤ 2.0 using |aba̅| ≤ 1.0 and |b̅ab| ≤ 1.0
11. • |a̅aba̅b̅aba| ≤ 2.0 using |aba̅b̅ab| ≤ 2.0
12. • |ba̅b̅aaba̅b̅aba̅| ≤ 3.0 using |ba̅b̅| ≤ 1.0 and |aaba̅b̅aba̅| ≤ 2.0
13. • |a̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 4.0 using |a̅b̅a| ≤ 1.0 and |ba̅b̅aaba̅b̅aba̅| ≤ 3.0
14. • |b̅a̅b̅aba̅b̅aaba̅b̅aba̅b| ≤ 4.0 using |a̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 4.0
15. • |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 6.0 using |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅| ≤ 4.0 and |aaba̅b̅aba̅| ≤ 2.0
16. • |b̅aba̅b̅a| ≤ 2.0 using |b̅ab| ≤ 1.0 and |a̅b̅a| ≤ 1.0
17. • |ab̅aba̅b̅aa̅| ≤ 2.0 using |b̅aba̅b̅a| ≤ 2.0
18. • |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 8.0 using |a̅b̅aba̅b̅aa| ≤ 2.0 and |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 6.0
19. • |b̅a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b| ≤ 8.0 using |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 8.0
20. • |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 10.0 using |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅| ≤ 8.0 and |aaba̅b̅aba̅| ≤ 2.0
21. • |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 12.0 using |a̅b̅aba̅b̅aa| ≤ 2.0 and |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 10.0
22. • |b̅a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b| ≤ 12.0 using |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 12.0
23. • |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 14.0 using |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅| ≤ 12.0 and |aaba̅b̅aba̅| ≤ 2.0
24. • |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 16.0 using |a̅b̅aba̅b̅aa| ≤ 2.0 and |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 14.0
25. • |b̅a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b| ≤ 16.0 using |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 16.0
26. • |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 18.0 using |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅| ≤ 16.0 and |aaba̅b̅aba̅| ≤ 2.0
27. • |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 20.0 using |a̅b̅aba̅b̅aa| ≤ 2.0 and |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 18.0
28. • |b̅a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b| ≤ 20.0 using |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 20.0
29. • |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 22.0 using |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅| ≤ 20.0 and |aaba̅b̅aba̅| ≤ 2.0
30. • |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 24.0 using |a̅b̅aba̅b̅aa| ≤ 2.0 and |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 22.0
31. • |b̅a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b| ≤ 24.0 using |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 24.0
32. • |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 26.0 using |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅| ≤ 24.0 and |aaba̅b̅aba̅| ≤ 2.0
33. • |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 28.0 using |a̅b̅aba̅b̅aa| ≤ 2.0 and |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 26.0
34. • |b̅a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b| ≤ 28.0 using |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 28.0
35. • |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 30.0 using |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅| ≤ 28.0 and |aaba̅b̅aba̅| ≤ 2.0
36. • |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 32.0 using |a̅b̅aba̅b̅aa| ≤ 2.0 and |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 30.0
37. • |b̅a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b| ≤ 32.0 using |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 32.0
38. • |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 34.0 using |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅| ≤ 32.0 and |aaba̅b̅aba̅| ≤ 2.0
39. • |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 36.0 using |a̅b̅aba̅b̅aa| ≤ 2.0 and |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 34.0
40. • |b̅a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b| ≤ 36.0 using |a̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅| ≤ 36.0
41. • |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅a| ≤ 37.0 using |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅| ≤ 36.0 and |a| ≤ 1.0
42. • |aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅a| ≤ 38.0 using |a| ≤ 1.0 and |ba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅a| ≤ 37.0
43. • |aba̅b̅aba̅b̅a| ≤ 2.111111111111111 using |aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅aaba̅b̅aba̅b̅a| ≤ 38.0 by taking 18th power
44. • |baba̅b̅aba̅b̅ab̅| ≤ 2.111111111111111 using |aba̅b̅aba̅b̅a| ≤ 2.111111111111111
45. • |aa| ≤ 2.0 using |a| ≤ 1.0 and |a| ≤ 1.0
46. • |baab̅| ≤ 2.0 using |aa| ≤ 2.0
47. • |aba̅b̅aab| ≤ 3.0 using |aba̅| ≤ 1.0 and |b̅aab| ≤ 2.0
48. • |a̅aba̅b̅aaba| ≤ 3.0 using |aba̅b̅aab| ≤ 3.0
49. • |aaba̅b̅aaba̅b̅aab| ≤ 5.0 using |aaba̅b̅aaba̅| ≤ 3.0 and |b̅aab| ≤ 2.0
50. • |a̅b̅aaba̅| ≤ 2.0 using |a̅b̅a| ≤ 1.0 and |aba̅| ≤ 1.0
51. • |b̅a̅b̅aaba̅b| ≤ 2.0 using |a̅b̅aaba̅| ≤ 2.0
52. • |ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aab| ≤ 7.0 using |ba̅b̅aaba̅b̅| ≤ 2.0 and |aaba̅b̅aaba̅b̅aab| ≤ 5.0
53. • |a̅ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba| ≤ 7.0 using |ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aab| ≤ 7.0
54. • |a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅| ≤ 8.0 using |a̅b̅a| ≤ 1.0 and |aba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅| ≤ 7.0
55. • |b̅a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b| ≤ 8.0 using |a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅| ≤ 8.0
56. • |b̅aaba̅b̅a| ≤ 3.0 using |b̅aab| ≤ 2.0 and |a̅b̅a| ≤ 1.0
57. • |ab̅aaba̅b̅aa̅| ≤ 3.0 using |b̅aaba̅b̅a| ≤ 3.0
58. • |a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅| ≤ 11.0 using |a̅b̅aaba̅b̅aa| ≤ 3.0 and |ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅| ≤ 8.0
59. • |b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅| ≤ 13.0 using |b̅aab| ≤ 2.0 and |a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅| ≤ 11.0
60. • |ab̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅a̅| ≤ 13.0 using |b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅| ≤ 13.0
61. • |b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅a| ≤ 15.0 using |b̅aab| ≤ 2.0 and |a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅a| ≤ 13.0
62. • |ab̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aa̅| ≤ 15.0 using |b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅a| ≤ 15.0
63. • |b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aa| ≤ 17.0 using |b̅aab| ≤ 2.0 and |a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aa| ≤ 15.0
64. • |aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aa| ≤ 20.0 using |aaba̅b̅aaba̅| ≤ 3.0 and |b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aa| ≤ 17.0
65. • |baaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aab̅| ≤ 20.0 using |aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aa| ≤ 20.0
66. • |aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aab| ≤ 23.0 using |aaba̅b̅aaba̅| ≤ 3.0 and |b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aab| ≤ 20.0
67. • |ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aab| ≤ 25.0 using |ba̅b̅aaba̅b̅| ≤ 2.0 and |aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aab| ≤ 23.0
68. • |a̅ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba| ≤ 25.0 using |ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aab| ≤ 25.0
69. • |a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅| ≤ 26.0 using |a̅b̅a| ≤ 1.0 and |aba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅| ≤ 25.0
70. • |b̅a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b| ≤ 26.0 using |a̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅| ≤ 26.0
71. • |ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅a| ≤ 27.0 using |ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅| ≤ 26.0 and |a| ≤ 1.0
72. • |aba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅a| ≤ 28.0 using |a| ≤ 1.0 and |ba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅a| ≤ 27.0
73. • |aba̅b̅a| ≤ 1.5555555555555556 using |aba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅aaba̅b̅a| ≤ 28.0 by taking 18th power
74. • |baba̅b̅ab̅| ≤ 1.5555555555555556 using |aba̅b̅a| ≤ 1.5555555555555556
75. • |aba̅b̅aba̅b̅ab| ≤ 2.5555555555555554 using |aba̅| ≤ 1.0 and |b̅aba̅b̅ab| ≤ 1.5555555555555556
76. • |a̅aba̅b̅aba̅b̅aba| ≤ 2.5555555555555554 using |aba̅b̅aba̅b̅ab| ≤ 2.5555555555555554
77. • |aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 4.666666666666666 using |aaba̅b̅aba̅b̅aba̅| ≤ 2.5555555555555554 and |b̅aba̅b̅aba̅b̅ab| ≤ 2.111111111111111
78. • |aba̅b̅aba̅b̅aba̅b̅ab| ≤ 3.111111111111111 using |aba̅| ≤ 1.0 and |b̅aba̅b̅aba̅b̅ab| ≤ 2.111111111111111
79. • |ba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 4.111111111111111 using |ba̅b̅| ≤ 1.0 and |aba̅b̅aba̅b̅aba̅b̅ab| ≤ 3.111111111111111
80. • |a̅ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba| ≤ 4.111111111111111 using |ba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 4.111111111111111
81. • |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 5.111111111111111 using |ba̅b̅| ≤ 1.0 and |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 4.111111111111111
82. • |b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 3.111111111111111 using |b̅aba̅b̅aba̅b̅ab| ≤ 2.111111111111111 and |a̅b̅a| ≤ 1.0
83. • |ab̅aba̅b̅aba̅b̅aba̅b̅aa̅| ≤ 3.111111111111111 using |b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 3.111111111111111
84. • |a̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 8.222222222222221 using |a̅b̅aba̅b̅aba̅b̅aba̅b̅aa| ≤ 3.111111111111111 and |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 5.111111111111111
85. • |b̅a̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b| ≤ 8.222222222222221 using |a̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 8.222222222222221
86. • |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 12.888888888888888 using |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 8.222222222222221 and |aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 4.666666666666666
87. • |a̅ba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba| ≤ 12.888888888888888 using |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 12.888888888888888
88. • |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 13.888888888888888 using |ba̅b̅| ≤ 1.0 and |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 12.888888888888888
89. • |a̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅| ≤ 4.111111111111111 using |a̅b̅aba̅b̅aba̅b̅aba̅b̅aa| ≤ 3.111111111111111 and |ba̅b̅| ≤ 1.0
90. • |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅| ≤ 5.666666666666666 using |b̅aba̅b̅ab| ≤ 1.5555555555555556 and |a̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅| ≤ 4.111111111111111
91. • |ab̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅a̅| ≤ 5.666666666666666 using |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅| ≤ 5.666666666666666
92. • |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 19.555555555555554 using |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅a| ≤ 5.666666666666666 and |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 13.888888888888888
93. • |b̅a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b| ≤ 19.555555555555554 using |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 19.555555555555554
94. • |a̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 22.666666666666664 using |a̅b̅aba̅b̅aba̅b̅aba̅b̅aa| ≤ 3.111111111111111 and |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 19.555555555555554
95. • |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 23.666666666666664 using |b̅ab| ≤ 1.0 and |a̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 22.666666666666664
96. • |ab̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a̅| ≤ 23.666666666666664 using |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 23.666666666666664
97. • |b̅aba̅b̅aba̅b̅a| ≤ 2.5555555555555554 using |b̅aba̅b̅ab| ≤ 1.5555555555555556 and |a̅b̅a| ≤ 1.0
98. • |ab̅aba̅b̅aba̅b̅aa̅| ≤ 2.5555555555555554 using |b̅aba̅b̅aba̅b̅a| ≤ 2.5555555555555554
99. • |a̅b̅aba̅b̅aba̅b̅aaba̅b̅| ≤ 3.5555555555555554 using |a̅b̅aba̅b̅aba̅b̅aa| ≤ 2.5555555555555554 and |ba̅b̅| ≤ 1.0
100. • |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅| ≤ 5.666666666666666 using |b̅aba̅b̅aba̅b̅ab| ≤ 2.111111111111111 and |a̅b̅aba̅b̅aba̅b̅aaba̅b̅| ≤ 3.5555555555555554
101. • |aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 5.111111111111111 using |aaba̅b̅aba̅| ≤ 2.0 and |b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 3.111111111111111
102. • |baaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab̅| ≤ 5.111111111111111 using |aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 5.111111111111111
103. • |b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 6.111111111111111 using |b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 5.111111111111111 and |a̅b̅a| ≤ 1.0
104. • |ab̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aa̅| ≤ 6.111111111111111 using |b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 6.111111111111111
105. • |b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aa| ≤ 8.222222222222221 using |b̅aba̅b̅aba̅b̅ab| ≤ 2.111111111111111 and |a̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aa| ≤ 6.111111111111111
106. • |aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aa| ≤ 10.777777777777777 using |aaba̅b̅aba̅b̅aba̅| ≤ 2.5555555555555554 and |b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aa| ≤ 8.222222222222221
107. • |baaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aab̅| ≤ 10.777777777777777 using |aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aa| ≤ 10.777777777777777
108. • |b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅a| ≤ 16.444444444444443 using |b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aab| ≤ 10.777777777777777 and |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅a| ≤ 5.666666666666666
109. • |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 24.22222222222222 using |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 19.555555555555554 and |aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 4.666666666666666
110. • |a̅ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba| ≤ 24.22222222222222 using |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 24.22222222222222
111. • |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 47.888888888888886 using |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 23.666666666666664 and |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 24.22222222222222
112. • |b̅a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b| ≤ 47.888888888888886 using |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 47.888888888888886
113. • |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 52.55555555555555 using |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 47.888888888888886 and |aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 4.666666666666666
114. • |a̅ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba| ≤ 52.55555555555555 using |ba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 52.55555555555555
115. • |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅a| ≤ 69.0 using |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅| ≤ 52.55555555555555 and |b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅a| ≤ 16.444444444444443
116. • |baba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅ab̅| ≤ 69.0 using |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅a| ≤ 69.0
117. • |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 92.66666666666666 using |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅ab| ≤ 69.0 and |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 23.666666666666664
118. • |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 93.66666666666666 using |aba̅| ≤ 1.0 and |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 92.66666666666666
119. • |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 4.9298245614035086 using |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aaba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 93.66666666666666 by taking 19th power
120. • |baba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab̅| ≤ 4.9298245614035086 using |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 4.9298245614035086
121. • |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 6.9298245614035086 using |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 4.9298245614035086 and |a̅b̅aba̅b̅| ≤ 2.0
122. • |ab̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a̅| ≤ 6.9298245614035086 using |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 6.9298245614035086
123. • |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 7.9298245614035086 using |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅a| ≤ 6.9298245614035086 and |ba̅b̅| ≤ 1.0
124. • |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 12.859649122807017 using |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅ab| ≤ 4.9298245614035086 and |a̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 7.9298245614035086
125. • |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 13.859649122807017 using |aba̅| ≤ 1.0 and |b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 12.859649122807017
126. • |aba̅b̅| ≤ 0.8152734778121775 using |aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅aba̅b̅| ≤ 13.859649122807017 by taking 17th power