#8061 ⟨a, b | aaa=1, abab=bbb⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

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
#RuleProof
1. b11 ⇒ b5 [9]
2. bab9 ⇒ bab3 [8]
3. b2ab8 ⇒ b2ab2 [7]
4. b3ab ⇒ ab4 [4]
5. a2b3 ⇒ bab [3]
6. (ab)2 ⇒ b3 [2]
7. (ab2)2 ⇒ b2ab4 [5]
8. (bab)2 ⇒ ab6 [6]
9. a3 ⇒ 1 [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

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