#675 ⟨a, b | aababbbba=1⟩

Up:Monoids with two generators and one relation
Prev:#674 ⟨a, b | aababbbab=1⟩
Next:#676 ⟨a, b | aabbaaaab=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. dc ⇒ 1
  2. cd ⇒ 1
  3. ca ⇒ ac
  4. da ⇒ ad
  5. a3 ⇒ c
  6. bcba ⇒ cbab
  7. baba2 ⇒ d(bc)2
  8. bab2a2 ⇒ db(bc)2
  9. b4c ⇒ a2bab3
  10. bab3d ⇒ adb4
  11. b4ac ⇒ a2bab3a
  12. bab3ad ⇒ adb4a
  13. b4a2 ⇒ a2db3cb
  14. bab3a2 ⇒ db3cbc
  15. bab4 ⇒ d 
# ab:aababbbba=1 reversed:cda/b aaa=c,babbbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bcba=cbab
babaa=dbcbc
babbaa=dbbcbc
bbbbc=aababbb
babbbd=adbbbb
bbbbac=aababbba
babbbad=adbbbba
bbbbaa=aadbbbcb
babbbaa=dbbbcbc
babbbb=d

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other anti-isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
9691⟨a, b | aabbbbaba=1⟩φ(a) = a, φ(b) = b