#16582 ⟨a, b | aaaa=1, aababbb=1⟩

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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. b16 ⇒ 1
  2. a2 ⇒ bab3
  3. aba ⇒ b4ab
  4. ab2a ⇒ b8ab14
  5. ab3a ⇒ b3ab4
  6. ab4a ⇒ b12
  7. ab5a ⇒ b12ab13
  8. ab6a ⇒ b2ab8
  9. ab7a ⇒ b15ab12
  10. ab8a ⇒ b13ab15
  11. ab9a ⇒ b7ab6
  12. ab10a ⇒ b9ab5
  13. ab11a ⇒ b5ab10
  14. ab12a ⇒ b14ab2
  15. ab13a ⇒ b6ab11
  16. ab14a ⇒ b11ab7
  17. ab15a ⇒ b10ab9 
# ab:aaaa=1,aababbb=1 b/a
bbbbbbbbbbbbbbbb=1
aa=babbb
aba=bbbbab
abba=bbbbbbbbabbbbbbbbbbbbbb
abbba=bbbabbbb
abbbba=bbbbbbbbbbbb
abbbbba=bbbbbbbbbbbbabbbbbbbbbbbbb
abbbbbba=bbabbbbbbbb
abbbbbbba=bbbbbbbbbbbbbbbabbbbbbbbbbbb
abbbbbbbba=bbbbbbbbbbbbbabbbbbbbbbbbbbbb
abbbbbbbbba=bbbbbbbabbbbbb
abbbbbbbbbba=bbbbbbbbbabbbbb
abbbbbbbbbbba=bbbbbabbbbbbbbbb
abbbbbbbbbbbba=bbbbbbbbbbbbbbabb
abbbbbbbbbbbbba=bbbbbbabbbbbbbbbbb
abbbbbbbbbbbbbba=bbbbbbbbbbbabbbbbbb
abbbbbbbbbbbbbbba=bbbbbbbbbbabbbbbbbbb

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.

6 total

Σ#PresentationMapping
1116600⟨a, b | aaaa=1, ababbba=1⟩φ(a) = a, φ(b) = b
1116607⟨a, b | aaaa=1, abbbaab=1⟩φ(a) = a, φ(b) = b
1116617⟨a, b | aaaa=1, baababb=1⟩φ(a) = a, φ(b) = b
1117146⟨a, b | aaaa=1, baabbb=a⟩φ(a) = a, φ(b) = abbbbbbbbbbb
1117148⟨a, b | aaaa=1, bababb=a⟩φ(a) = a, φ(b) = abbbbbbb
1117678⟨a, b | aaaa=1, babbb=aa⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

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

3 total

Σ#PresentationMapping
1116587⟨a, b | aaaa=1, aabbbab=1⟩φ(a) = a, φ(b) = b
1116595⟨a, b | aaaa=1, abaabbb=1⟩φ(a) = a, φ(b) = b
1116620⟨a, b | aaaa=1, babaabb=1⟩φ(a) = a, φ(b) = b