#20884 ⟨a, b | bb=aa, aaaaa=aa⟩

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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. b8 ⇒ b2 [6]
2. ab2 ⇒ b6 [5]
3. b2a ⇒ b6 [7]
4. a2 ⇒ b2 [1]
# ab:bb=aa,aaaaa=aa b/a
bbbbbbbb=bb
abb=bbbbbb
bba=bbbbbb
aa=bb

Isomorphic instances

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

17 total

Σ#PresentationMapping
1120886⟨a, b | bb=aa, aaaaa=bb⟩φ(a) = a, φ(b) = b
1120887⟨a, b | bb=aa, aaaab=aa⟩φ(a) = b, φ(b) = a
1120890⟨a, b | bb=aa, aaaab=bb⟩φ(a) = b, φ(b) = a
1120891⟨a, b | bb=aa, aaaba=aa⟩φ(a) = b, φ(b) = a
1120894⟨a, b | bb=aa, aaaba=bb⟩φ(a) = b, φ(b) = a
1120895⟨a, b | bb=aa, aaabb=aa⟩φ(a) = a, φ(b) = b
1120898⟨a, b | bb=aa, aaabb=bb⟩φ(a) = a, φ(b) = b
1120899⟨a, b | bb=aa, aabaa=aa⟩φ(a) = b, φ(b) = a
1120901⟨a, b | bb=aa, aabaa=bb⟩φ(a) = b, φ(b) = a
1120902⟨a, b | bb=aa, aabab=aa⟩φ(a) = a, φ(b) = b
1120905⟨a, b | bb=aa, aabab=bb⟩φ(a) = a, φ(b) = b
1120906⟨a, b | bb=aa, aabba=aa⟩φ(a) = a, φ(b) = b
1120909⟨a, b | bb=aa, aabba=bb⟩φ(a) = a, φ(b) = b
1120910⟨a, b | bb=aa, abaab=aa⟩φ(a) = a, φ(b) = b
1120913⟨a, b | bb=aa, abaab=bb⟩φ(a) = a, φ(b) = b
1120917⟨a, b | bb=aa, abbba=aa⟩φ(a) = b, φ(b) = a
1120919⟨a, b | bb=aa, abbba=bb⟩φ(a) = b, φ(b) = a