#1636 ⟨a, b | aab=ba, abb=a⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-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. a5 ⇒ a2 [3]
2. ba ⇒ a2b [1]
3. ab2 ⇒ a [2]
# ab:aab=ba,abb=a reversed:a/b
aaaaa=aa
ba=aab
abb=a

Isomorphic instances

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

1 total

Σ#PresentationMapping
91681⟨a, b | aba=bb, baa=b⟩φ(a) = b, φ(b) = a

Anti-isomorphic instances

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

6 total

Σ#PresentationMapping
1119515⟨a, b | aab=b, aaaba=bb⟩φ(a) = b, φ(b) = a
1119518⟨a, b | aab=b, aaabb=ba⟩φ(a) = b, φ(b) = a
1119542⟨a, b | aab=b, abaab=ba⟩φ(a) = b, φ(b) = a
1120067⟨a, b | aab=b, aaba=abb⟩φ(a) = b, φ(b) = a
1120074⟨a, b | aab=b, aabb=aba⟩φ(a) = b, φ(b) = a
1120122⟨a, b | aab=b, baab=aba⟩φ(a) = b, φ(b) = a