#1228 ⟨a, b | aabba=abab⟩

Up:Monoids with two generators and one relation
Prev:#1227 ⟨a, b | aabba=abaa⟩
Next:#1229 ⟨a, b | aabba=abba⟩

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. (ab)2 ⇒ ac
  2. ab2a ⇒ c
  3. abc ⇒ acba
  4. abac ⇒ acab
  5. cbab ⇒ c2
  6. (ac)2ba ⇒ ac2b
  7. ab2c ⇒ cb2a
  8. cbc ⇒ c2ba
  9. cbac ⇒ c2ab
  10. ac2b2 ⇒ acac2
  11. ac3ba ⇒ acac2ab
  12. c2acba ⇒ c3b
  13. ac4a ⇒ acac3
  14. c3b2 ⇒ c2ac2
  15. acac2ab2 ⇒ ac4
  16. c4ba ⇒ (c2a)2b
  17. c5a ⇒ c2ac3
  18. aca(c2a)2 ⇒ ac5
  19. (c2a)2b2 ⇒ c5
  20. (c2a)3 ⇒ c6 
# ab:aabba=abab reversed:a/bc abba=c frequency:4/0
abab=ac
abba=c
abc=acba
abac=acab
cbab=cc
acacba=accb
abbc=cbba
cbc=ccba
cbac=ccab
accbb=acacc
acccba=acaccab
ccacba=cccb
acccca=acaccc
cccbb=ccacc
acaccabb=acccc
ccccba=ccaccab
ccccca=ccaccc
acaccacca=accccc
ccaccabb=ccccc
ccaccacca=cccccc

Right Cayley graph (truncated)

Left Cayley graph (truncated)