#15435 ⟨a, b | aaa=aa, babbb=a⟩

Up:Monoids with two generators and two relations
Prev:#15434 ⟨a, b | aaa=aa, babab=b⟩
Next:#15436 ⟨a, b | aaa=aa, babbb=b⟩

Properties

Complete 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
  1. a3 ⇒ a2
  2. aba2 ⇒ ba2
  3. a(ba)2 ⇒ (ba)2
  4. ba2ba ⇒ (ba)2
  5. ab2a2 ⇒ b2a2
  6. bab2a ⇒ a2b3
  7. ba2b2a ⇒ a2b3
  8. ab(ba)2 ⇒ b(ba)2
  9. b3a2 ⇒ a2b3a
  10. bab3 ⇒ a
  11. ba2b3a ⇒ a2
  12. b3aba ⇒ a2b4a
  13. a2b5a ⇒ b2a2b3
  14. ba2b4a ⇒ a2ba
  15. a2b6 ⇒ (ba)2 
# ab:aaa=aa,babbb=a reversed:a/b
aaa=aa
abaa=baa
ababa=baba
baaba=baba
abbaa=bbaa
babba=aabbb
baabba=aabbb
abbaba=bbaba
bbbaa=aabbba
babbb=a
baabbba=aa
bbbaba=aabbbba
aabbbbba=bbaabbb
baabbbba=aaba
aabbbbbb=baba

Right Cayley graph (truncated)

Left Cayley graph (truncated)