#1513 ⟨a, b | ababababba=1⟩

Up:Monoids with two generators and one relation
Prev:#1512 ⟨a, b | ababababab=1⟩
Next:#1514 ⟨a, b | abababbaab=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 ⇒ cd
  2. c4d ⇒ 1
  3. db ⇒ bc
  4. c4b ⇒ bc3d
  5. ca ⇒ ad
  6. da ⇒ ac16
  7. ba ⇒ d
  8. ab ⇒ c 
# ab:ababababba=1 cd/ba ab=c,ba=d frequency:2/0,2/2
dc=cd
ccccd=1
db=bc
ccccb=bcccd
ca=ad
da=acccccccccccccccc
ba=d
ab=c

Right Cayley graph (truncated)

Left Cayley graph (truncated)