#3017 ⟨a, b | aa=a, abab=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. a2 ⇒ a [1]
2. aba ⇒ ba [3]
3. bab ⇒ ba [4]
4. b2a ⇒ ba [5]
# ab:aa=a,abab=ba ab
aa=a
aba=ba
bab=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
108860⟨a, b | aa=a, aabab=ba⟩φ(a) = a, φ(b) = b
108872⟨a, b | aa=a, abaab=ba⟩φ(a) = a, φ(b) = b
109146⟨a, b | aa=a, abab=baa⟩φ(a) = a, φ(b) = b
1124609⟨a, b | aa=a, aaabab=ba⟩φ(a) = a, φ(b) = b
1124621⟨a, b | aa=a, aabaab=ba⟩φ(a) = a, φ(b) = b
1124648⟨a, b | aa=a, abaaab=ba⟩φ(a) = a, φ(b) = b
1125156⟨a, b | aa=a, aabab=baa⟩φ(a) = a, φ(b) = b
1125180⟨a, b | aa=a, abaab=baa⟩φ(a) = a, φ(b) = b
1125688⟨a, b | aa=a, baaa=abab⟩φ(a) = a, φ(b) = b