#27121 ⟨a, b | aa=1, ababbab=bb⟩

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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. b6 ⇒ b2 [14]
2. b2ab5 ⇒ b2ab [12]
3. b4ab ⇒ ab5 [13]
4. a2 ⇒ 1 [1]
5. abab2 ⇒ bab4 [4]
6. ab2ab ⇒ b3ab2 [11]
7. ab3ab ⇒ b2ab4 [5]
8. b2(ab)2 ⇒ b3ab3 [15]
# ab:aa=1,ababbab=bb b/a
bbbbbb=bb
bbabbbbb=bbab
bbbbab=abbbbb
aa=1
ababb=babbbb
abbab=bbbabb
abbbab=bbabbbb
bbabab=bbbabbb

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
1127737⟨a, b | aa=1, babbab=abb⟩φ(a) = a, φ(b) = b