#1452 ⟨a, b | aabbabbaab=1⟩

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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. ab2 ⇒ cbc
  2. a2b ⇒ cac
  3. bc2a ⇒ cacb
  4. bca2 ⇒ c2ac
  5. b2ca ⇒ cbc2
  6. acbc ⇒ cacb
  7. c2acb ⇒ 1
  8. bc3bc ⇒ cacb3
  9. bc3ac ⇒ cacbab
  10. bc(ac)2 ⇒ c(ca)2b
  11. b2c2bc ⇒ cbc2b2
  12. ac3ac ⇒ cacba2
  13. abcbc2 ⇒ c(bc)2a
  14. abcacb ⇒ cbc3a
  15. a2c2ac ⇒ cac2a2
  16. a(ac)2b ⇒ cac3a
  17. c2ac2bc2 ⇒ bca
  18. bc5ac ⇒ cacb3a2
  19. b2c4ac ⇒ cbc2b2a2
  20. abcac2bc2 ⇒ cbc3abca
  21. a2cac2bc2 ⇒ cac3abca 
# ab:aabbabbaab=1 cba abbaab=c frequency:6/4
abb=cbc
aab=cac
bcca=cacb
bcaa=ccac
bbca=cbcc
acbc=cacb
ccacb=1
bcccbc=cacbbb
bcccac=cacbab
bcacac=ccacab
bbccbc=cbccbb
acccac=cacbaa
abcbcc=cbcbca
abcacb=cbccca
aaccac=caccaa
aacacb=caccca
ccaccbcc=bca
bcccccac=cacbbbaa
bbccccac=cbccbbaa
abcaccbcc=cbcccabca
aacaccbcc=cacccabca

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

2 total

Σ#PresentationMapping
101501⟨a, b | abaabbabba=1⟩φ(a) = b, φ(b) = a
101502⟨a, b | abaabbbaab=1⟩φ(a) = b, φ(b) = ca