#27686 ⟨a, b | aa=1, abbbba=bab⟩

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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. b46 ⇒ b6
  2. bab42 ⇒ bab2
  3. b2ab41 ⇒ b2ab
  4. b5a ⇒ ab5
  5. a2 ⇒ 1
  6. (ab)2 ⇒ b4a
  7. ab4a ⇒ bab
  8. (ba)2 ⇒ ab4
  9. bab2a ⇒ ab3ab4
  10. bab3ab40 ⇒ bab3a
  11. b(b3a)2 ⇒ ab2ab
  12. a(b3a)2 ⇒ bab3ab36 
# ab:aa=1,abbbba=bab b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bbbbbb
babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=babb
bbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bbab
bbbbba=abbbbb
aa=1
abab=bbbba
abbbba=bab
baba=abbbb
babba=abbbabbbb
babbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=babbba
bbbbabbba=abbab
abbbabbba=babbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

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.

2 total

Σ#PresentationMapping
1128165⟨a, b | aa=1, ababa=bbbb⟩φ(a) = a, φ(b) = b
1128218⟨a, b | aa=1, abbbb=baba⟩φ(a) = a, φ(b) = b