#729 ⟨a, b | abbbabbba=1⟩

Up:Monoids with two generators and one relation
Prev:#728 ⟨a, b | abbbaaaab=1⟩
Next:#730 ⟨a, b | abbbbbbba=1⟩

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. a2 ⇒ c
  2. ca ⇒ ac
  3. cd ⇒ 1
  4. da ⇒ ad
  5. dc ⇒ 1
  6. db ⇒ abad2
  7. acb ⇒ bac
  8. c2b ⇒ abac
  9. ab3 ⇒ b3a
  10. cb3 ⇒ b3c
  11. b6 ⇒ ad2 
# ab:abbbabbba=1 acd/b aa=c,bbbabbb=d magic:0
aa=c
ca=ac
cd=1
da=ad
dc=1
db=abadd
acb=bac
ccb=abac
abbb=bbba
cbbb=bbbc
bbbbbb=add

Right Cayley graph (truncated)

Left Cayley graph (truncated)