#22799 ⟨a, b | aaa=1, ababb=bab⟩

Up:Monoids with two generators and two relations
Prev:#22793 ⟨a, b | aaa=1, ababa=bbb⟩
Next:#22800 ⟨a, b | aaa=1, ababb=bba⟩

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 [6]
2. b5ab ⇒ b2ab [13]
3. (ab)2 ⇒ bab3 [4]
4. ab4ab ⇒ b4ab3 [12]
5. bab3ab ⇒ ab2ab3 [7]
6. (b2a)2b ⇒ ab3ab2 [9]
7. a3 ⇒ 1 [1]
8. a2b2ab ⇒ b(ab2)2 [5]
9. ba2b3ab ⇒ a2b3ab2 [15]
# ab:aaa=1,ababb=bab b/a
babbbb=bab
bbbbbab=bbab
abab=babbb
abbbbab=bbbbabbb
babbbab=abbabbb
bbabbab=abbbabb
aaa=1
aabbab=babbabb
baabbbab=aabbbabb