#3122 ⟨a, b | ab=a, bbaa=ba⟩

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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. ab ⇒ a [1]
2. a3 ⇒ a2 [3]
3. ba2 ⇒ ba [4]
4. b2a ⇒ ba [5]
# ab:ab=a,bbaa=ba ab
ab=a
aaa=aa
baa=ba
bba=ba

Isomorphic instances

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

9 total

Σ#PresentationMapping
109086⟨a, b | ab=a, bbaab=ba⟩φ(a) = a, φ(b) = b
109090⟨a, b | ab=a, bbaba=ba⟩φ(a) = a, φ(b) = b
109357⟨a, b | ab=a, bbaa=bab⟩φ(a) = a, φ(b) = b
1125066⟨a, b | ab=a, bbaabb=ba⟩φ(a) = a, φ(b) = b
1125074⟨a, b | ab=a, bbabab=ba⟩φ(a) = a, φ(b) = b
1125078⟨a, b | ab=a, bbabba=ba⟩φ(a) = a, φ(b) = b
1125609⟨a, b | ab=a, bbaab=bab⟩φ(a) = a, φ(b) = b
1125617⟨a, b | ab=a, bbaba=bab⟩φ(a) = a, φ(b) = b
1125869⟨a, b | ab=a, bbaa=babb⟩φ(a) = a, φ(b) = b