#19836 ⟨a, b | aaa=a, babb=aba⟩

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  1. Properties
  2. Rewriting system

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. bab6 ⇒ bab2 [3]
2. aba ⇒ bab2 [2]
3. (ab2)2 ⇒ bab3a [5]
4. bab3ab4 ⇒ bab3a [7]
5. (bab4)2 ⇒ bab5a [9]
6. a3 ⇒ a [1]
7. bab2a2 ⇒ bab2 [4]
8. bab4a2 ⇒ bab4 [6]
9. b(b3a)3 ⇒ a(b3a)2 [32]
10. (b5a)2b3a ⇒ bab5ab3a [27]
11. b(b4a)2b5a ⇒ bab4ab5a [26]
12. bab3a2b2 ⇒ a(b3a)2 [8]
13. (b5a)2ab2 ⇒ bab5a2b2 [28]
14. a(b3ab)2b ⇒ (b3a)3 [35]
15. bab5a2b6 ⇒ bab5a2b2 [12]
16. a2(b3a)2 ⇒ bab5a2b2 [10]
17. a(b3a)3 ⇒ bab5a2b3a [39]
18. ab(b2ab3)2a ⇒ (b4a)2b5a [31]
19. ab4ab5ab3a ⇒ b3ab5a2b2 [41]
20. b(ab5a)2 ⇒ (b3a)3 [25]
21. (ab4)3ba ⇒ b(b2ab3)2a [33]
22. ab3ab5a2b2 ⇒ b4ab5ab3a [34]
23. ab4ab5a2b2 ⇒ b3ab5a2b3a [36]
24. bab5a2b4ab2 ⇒ bab4ab5a [40]
25. bab5a2b3ab4 ⇒ bab5a2b3a [15]
26. bab3(b2a2)2 ⇒ bab5a2b2 [13]
27. bab(b4a2)2 ⇒ bab5a2b4 [14]
28. bab4(ba2b2)2 ⇒ b(b2ab3)2a [16]
# ab:aaa=a,babb=aba reversed:b/a
babbbbbb=babb
aba=babb
abbabb=babbba
babbbabbbb=babbba
babbbbbabbbb=babbbbba
aaa=a
babbaa=babb
babbbbaa=babbbb
bbbbabbbabbba=abbbabbba
bbbbbabbbbbabbba=babbbbbabbba
bbbbbabbbbabbbbba=babbbbabbbbba
babbbaabb=abbbabbba
bbbbbabbbbbaabb=babbbbbaabb
abbbabbbbabb=bbbabbbabbba
babbbbbaabbbbbb=babbbbbaabb
aabbbabbba=babbbbbaabb
abbbabbbabbba=babbbbbaabbba
abbbabbbbbabbba=bbbbabbbbabbbbba
abbbbabbbbbabbba=bbbabbbbbaabb
babbbbbaabbbbba=bbbabbbabbba
abbbbabbbbabbbbba=bbbabbbbbabbba
abbbabbbbbaabb=bbbbabbbbbabbba
abbbbabbbbbaabb=bbbabbbbbaabbba
babbbbbaabbbbabb=babbbbabbbbba
babbbbbaabbbabbbb=babbbbbaabbba
babbbbbaabbaa=babbbbbaabb
babbbbbaabbbbaa=babbbbbaabbbb
babbbbbaabbbaabb=bbbabbbbbabbba