#5383 ⟨a, b | aab=ab, bab=aa⟩

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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. a3 ⇒ a2 [5]
2. ab ⇒ ba2 [7]
3. b2a2 ⇒ a2 [6]
# ab:aab=ab,bab=aa a/b
aaa=aa
ab=baa
bbaa=aa

Isomorphic instances

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

4 total

Σ#PresentationMapping
105418⟨a, b | aba=ab, bab=aa⟩φ(a) = a, φ(b) = b
1116181⟨a, b | aab=ab, baab=aa⟩φ(a) = a, φ(b) = b
1116409⟨a, b | aba=ab, baab=aa⟩φ(a) = a, φ(b) = b
1116413⟨a, b | aba=ab, baba=aa⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

6 total

Σ#PresentationMapping
105402⟨a, b | aab=ba, bba=aa⟩φ(a) = a, φ(b) = b
1116229⟨a, b | aab=ba, abab=aa⟩φ(a) = a, φ(b) = b
1116245⟨a, b | aab=ba, baab=aa⟩φ(a) = a, φ(b) = b
1116249⟨a, b | aab=ba, baba=aa⟩φ(a) = a, φ(b) = b
1116282⟨a, b | aab=bb, aaba=ab⟩φ(a) = b, φ(b) = a
1116445⟨a, b | aba=bb, aaba=ab⟩φ(a) = b, φ(b) = a