#1352 ⟨a, b | aaababaaba=1⟩

Up:Monoids with two generators and one relation
Prev:#1351 ⟨a, b | aaababaaab=1⟩
Next:#1353 ⟨a, b | aaababaabb=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. cd ⇒ dc
  2. ad ⇒ da
  3. ac ⇒ ca
  4. a2 ⇒ c
  5. dc2 ⇒ 1
  6. cbab ⇒ bc2bdca
  7. abcb ⇒ cbc2bda
  8. abc2b ⇒ (bc)2a
  9. d(cb)2 ⇒ (ab)2dc
  10. dcbc2b ⇒ (ba)2
  11. c(ab)2 ⇒ (bc)2
  12. bcbc2b ⇒ dca
  13. cb2cb ⇒ bc2bcabda
  14. ab2c2b ⇒ cbc2bdcba
  15. dcb2c2b ⇒ (ab)2dcaba
  16. cab2cb ⇒ bcbc3bda
  17. cb3c2b ⇒ bc2bcabdcba
  18. cab3c2b ⇒ bcbc3bdcba 
# ab:aaababaaba=1 dca/b aa=c,babcb=d frequency:2/0,5/0
cd=dc
ad=da
ac=ca
aa=c
dcc=1
cbab=bccbdca
abcb=cbccbda
abccb=bcbca
dcbcb=ababdc
dcbccb=baba
cabab=bcbc
bcbccb=dca
cbbcb=bccbcabda
abbccb=cbccbdcba
dcbbccb=ababdcaba
cabbcb=bcbcccbda
cbbbccb=bccbcabdcba
cabbbccb=bcbcccbdcba

Right Cayley graph (truncated)

Left Cayley graph (truncated)