#7799 ⟨a, b | aaa=1, abbba=bb⟩

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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. b32 ⇒ b2
  2. b2ab30 ⇒ b2a
  3. b5a ⇒ ab5
  4. a2b2 ⇒ b3a
  5. abab2 ⇒ b2ab29
  6. ab3a ⇒ b2
  7. b2a2 ⇒ ab3
  8. b(ba)2 ⇒ b4ab27
  9. (b2a)2 ⇒ ab4ab3
  10. b3ab4a ⇒ (ab2)2
  11. a3 ⇒ 1
  12. bab2ab4a ⇒ ab2ab4ab19 
# ab:aaa=1,abbba=bb b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bb
bbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bba
bbbbba=abbbbb
aabb=bbba
ababb=bbabbbbbbbbbbbbbbbbbbbbbbbbbbbbb
abbba=bb
bbaa=abbb
bbaba=bbbbabbbbbbbbbbbbbbbbbbbbbbbbbbb
bbabba=abbbbabbb
bbbabbbba=abbabb
aaa=1
babbabbbba=abbabbbbabbbbbbbbbbbbbbbbbbb

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.

1 total

Σ#PresentationMapping
1123316⟨a, b | aaa=1, bbaa=abbb⟩φ(a) = a, φ(b) = b