#1431 ⟨a, b | aababbabba=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. bc ⇒ cb
  2. cb2 ⇒ 1
  3. ca2ba ⇒ a3cb
  4. ba(b2a)2 ⇒ ab(ab2)2
  5. cba2ba ⇒ ba3cb
  6. c(ba)2b2a ⇒ a(b2a)2c
  7. b2a3 ⇒ a(ab)2
  8. ba3ba ⇒ (ab2)2a2c
  9. (ba)3b2a ⇒ abab2ab4ac
  10. a3bab2a ⇒ c
  11. b(aba)2b2a ⇒ abab2ab4a2c
  12. cba(ab2)2a2 ⇒ a(b2a)2ca2b
  13. ca3(b2a)2a ⇒ (a3b)2
  14. (ba)2(ab2)2a2 ⇒ abab2ab4aca2b
  15. cba3(b2a)2a ⇒ (ab2)2a2ca2b
  16. a4(b2a)2a ⇒ ca2b
  17. baba3(b2a)2a ⇒ abab2ab4a2ca2b 
# ab:aababbabba=1 cb/a aaababba=c frequency:8/2
bc=cb
cbb=1
caaba=aaacb
babbabba=ababbabb
cbaaba=baaacb
cbababba=abbabbac
bbaaa=aabab
baaaba=abbabbaac
babababba=ababbabbbbac
aaababba=c
babaababba=ababbabbbbaac
cbaabbabbaa=abbabbacaab
caaabbabbaa=aaabaaab
babaabbabbaa=ababbabbbbacaab
cbaaabbabbaa=abbabbaacaab
aaaabbabbaa=caab
babaaabbabbaa=ababbabbbbaacaab

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
101497⟨a, b | abaababbba=1⟩φ(a) = b, φ(b) = a