#8061 ⟨a, b | aaa=1, abab=bbb⟩

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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. b11 ⇒ b5
  2. bab9 ⇒ bab3
  3. b2ab8 ⇒ b2ab2
  4. b3ab ⇒ ab4
  5. a2b3 ⇒ bab
  6. (ab)2 ⇒ b3
  7. (ab2)2 ⇒ b2ab4
  8. (bab)2 ⇒ ab6
  9. a3 ⇒ 1 
# ab:aaa=1,abab=bbb b/a
bbbbbbbbbbb=bbbbb
babbbbbbbbb=babbb
bbabbbbbbbb=bbabb
bbbab=abbbb
aabbb=bab
abab=bbb
abbabb=bbabbbb
babbab=abbbbbb
aaa=1

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
1122777⟨a, b | aaa=1, aabbb=bab⟩φ(a) = a, φ(b) = b