#1672 ⟨a, b | aba=ab, bba=a⟩

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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. ab3 ⇒ ab [4]
2. b2a ⇒ a [2]
3. a2 ⇒ ab2 [3]
4. aba ⇒ ab [1]
# ab:aba=ab,bba=a b/a
abbb=ab
bba=a
aa=abb
aba=ab

Isomorphic instances

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

4 total

Σ#PresentationMapping
1119526⟨a, b | aab=b, aabab=ba⟩φ(a) = b, φ(b) = a
1119574⟨a, b | aab=b, baaab=ba⟩φ(a) = b, φ(b) = a
1120069⟨a, b | aab=b, aaba=bab⟩φ(a) = b, φ(b) = a
1120090⟨a, b | aab=b, abab=aba⟩φ(a) = b, φ(b) = a