#26619 ⟨a, b | aa=1, abbabbba=b⟩

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Properties

Element profile

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. b9 ⇒ b
  2. bab8 ⇒ ba
  3. b8a ⇒ ab8
  4. a2 ⇒ 1
  5. aba ⇒ b2ab3
  6. ab2a ⇒ bab5
  7. ab3a ⇒ b6ab
  8. ab4a ⇒ b4ab4
  9. ab5a ⇒ b7ab2
  10. ab6a ⇒ b3ab7
  11. ab7a ⇒ b5ab6 
# ab:aa=1,abbabbba=b b/a
bbbbbbbbb=b
babbbbbbbb=ba
bbbbbbbba=abbbbbbbb
aa=1
aba=bbabbb
abba=babbbbb
abbba=bbbbbbab
abbbba=bbbbabbbb
abbbbba=bbbbbbbabb
abbbbbba=bbbabbbbbbb
abbbbbbba=bbbbbabbbbbb

Right Cayley graph

Left Cayley graph

Other isomorphic instances

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

3 total

Σ#PresentationMapping
1127147⟨a, b | aa=1, abbabbb=ba⟩φ(a) = a, φ(b) = b
1127155⟨a, b | aa=1, abbbabb=ba⟩φ(a) = a, φ(b) = ab
1127756⟨a, b | aa=1, bbabbb=aba⟩φ(a) = a, φ(b) = b