#8067 ⟨a, b | aaa=1, abba=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. b32 ⇒ b2
  2. b2ab30 ⇒ b2a
  3. b5a ⇒ ab5
  4. a2b2 ⇒ b2ab29
  5. ab2a ⇒ b3
  6. ab4a ⇒ b3ab3
  7. b2a2 ⇒ b4ab27
  8. b(ba)2 ⇒ (ab3)2
  9. (b3a)2 ⇒ abab2
  10. a3 ⇒ 1
  11. a2bab2 ⇒ b2ab3ab27
  12. (ab)3b ⇒ bab3ab8
  13. (ba)2b3a ⇒ abab3ab19 
# ab:aaa=1,abba=bbb b/a
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bb
bbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bba
bbbbba=abbbbb
aabb=bbabbbbbbbbbbbbbbbbbbbbbbbbbbbbb
abba=bbb
abbbba=bbbabbb
bbaa=bbbbabbbbbbbbbbbbbbbbbbbbbbbbbbb
bbaba=abbbabbb
bbbabbba=ababb
aaa=1
aababb=bbabbbabbbbbbbbbbbbbbbbbbbbbbbbbbb
abababb=babbbabbbbbbbb
bababbba=ababbbabbbbbbbbbbbbbbbbbbb

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
1122778⟨a, b | aaa=1, aabbb=bba⟩φ(a) = a, φ(b) = b