#19844 ⟨a, b | aaa=a, bbbb=aba⟩

Up:Monoids with two generators and two relations
Prev:#19843 ⟨a, b | aaa=a, bbbb=aab⟩
Next:#19845 ⟨a, b | aaa=a, bbbb=abb⟩

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. b21 ⇒ b6 [8]
2. bab5 ⇒ ab9 [7]
3. b4ab4 ⇒ ab5 [6]
4. b5a ⇒ ab5 [5]
5. a2b4 ⇒ b4 [3]
6. aba ⇒ b4 [2]
7. b4a2 ⇒ b4 [4]
8. a3 ⇒ a [1]
# ab:aaa=a,bbbb=aba b/a
bbbbbbbbbbbbbbbbbbbbb=bbbbbb
babbbbb=abbbbbbbbb
bbbbabbbb=abbbbb
bbbbba=abbbbb
aabbbb=bbbb
aba=bbbb
bbbbaa=bbbb
aaa=a