#23309 ⟨a, b | aaa=1, babb=abab⟩

Up:Monoids with two generators and two relations
Prev:#23303 ⟨a, b | aaa=1, baba=abbb⟩
Next:#23310 ⟨a, b | aaa=1, babb=abba⟩

Quick links

  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. bab4 ⇒ bab [3]
2. b5ab ⇒ b2ab [13]
3. (ab)2 ⇒ bab2 [2]
4. ab4ab ⇒ b4ab2 [14]
5. (bab)2 ⇒ (ab2)2 [4]
6. (b3a)2b ⇒ ab3ab [12]
7. a3 ⇒ 1 [1]
8. a2b2ab ⇒ b(ab3)2 [7]
9. a(b2ab)2 ⇒ b(bab2)2 [6]
10. ba2b3ab ⇒ a2b3ab2 [15]
# ab:aaa=1,babb=abab b/a
babbbb=bab
bbbbbab=bbab
abab=babb
abbbbab=bbbbabb
babbab=abbabb
bbbabbbab=abbbab
aaa=1
aabbab=babbbabbb
abbabbbab=bbabbbabb
baabbbab=aabbbabb