#3141 ⟨a, b | aa=a, abb=aba⟩

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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. ab2 ⇒ aba [2]
# ab:aa=a,abb=aba ab
aa=a
abb=aba

Isomorphic instances

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

7 total

Σ#PresentationMapping
109129⟨a, b | aa=a, aaba=abb⟩φ(a) = a, φ(b) = b
109136⟨a, b | aa=a, aabb=aba⟩φ(a) = a, φ(b) = b
1125133⟨a, b | aa=a, aaaba=abb⟩φ(a) = a, φ(b) = b
1125140⟨a, b | aa=a, aaabb=aba⟩φ(a) = a, φ(b) = b
1125149⟨a, b | aa=a, aabaa=abb⟩φ(a) = a, φ(b) = b
1125665⟨a, b | aa=a, aabb=aaba⟩φ(a) = a, φ(b) = b
1125668⟨a, b | aa=a, abaa=aabb⟩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
109132⟨a, b | aa=a, aaba=bba⟩φ(a) = a, φ(b) = b
1125136⟨a, b | aa=a, aaaba=bba⟩φ(a) = a, φ(b) = b