#8886 ⟨a, b | aa=a, abbba=ab⟩

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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. a2 ⇒ a [1]
2. aba ⇒ ab [3]
3. ab2a ⇒ ab2 [4]
4. ab3 ⇒ ab [5]
# ab:aa=a,abbba=ab ab
aa=a
aba=ab
abba=abb
abbb=ab

Isomorphic instances

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

3 total

Σ#PresentationMapping
1124639⟨a, b | aa=a, aabbba=ab⟩φ(a) = a, φ(b) = b
1124662⟨a, b | aa=a, ababba=ab⟩φ(a) = a, φ(b) = b
1125207⟨a, b | aa=a, abbba=aab⟩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.

2 total

Σ#PresentationMapping
1124640⟨a, b | aa=a, aabbba=ba⟩φ(a) = a, φ(b) = b
1124663⟨a, b | aa=a, ababba=ba⟩φ(a) = a, φ(b) = b