#27655 ⟨a, b | aa=1, ababbb=bab⟩

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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. bab5 ⇒ bab
  2. b6ab ⇒ b2ab
  3. a2 ⇒ 1
  4. (ab)2 ⇒ bab3
  5. ab5ab ⇒ b5ab3
  6. bab3ab ⇒ ab2ab3
  7. b2ab4ab ⇒ ab4ab3
  8. b(b2a)2b ⇒ (ab3)2
  9. a(b2a)2b ⇒ (b2a)2b3 
# ab:aa=1,ababbb=bab b/a
babbbbb=bab
bbbbbbab=bbab
aa=1
abab=babbb
abbbbbab=bbbbbabbb
babbbab=abbabbb
bbabbbbab=abbbbabbb
bbbabbab=abbbabbb
abbabbab=bbabbabbb

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
1128265⟨a, b | aa=1, babbb=abab⟩φ(a) = a, φ(b) = b