#1117 ⟨a, b | aa=1, ababb=b⟩

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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 ⇒ 1 [1]
2. bab2 ⇒ ab [3]
3. b(ab)2 ⇒ b [4]
# ab:aa=1,ababb=b ab
aa=1
babb=ab
babab=b

Isomorphic instances

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

11 total

Σ#PresentationMapping
81198⟨a, b | aa=1, babb=ab⟩φ(a) = a, φ(b) = b
109679⟨a, b | aa=1, aaababb=b⟩φ(a) = a, φ(b) = b
109721⟨a, b | aa=1, abaaabb=b⟩φ(a) = a, φ(b) = b
109729⟨a, b | aa=1, ababaab=b⟩φ(a) = a, φ(b) = b
109968⟨a, b | aa=1, aababb=ab⟩φ(a) = a, φ(b) = b
1010003⟨a, b | aa=1, ababba=ba⟩φ(a) = a, φ(b) = b
1010032⟨a, b | aa=1, baaabb=ab⟩φ(a) = a, φ(b) = b
1010275⟨a, b | aa=1, ababb=aab⟩φ(a) = a, φ(b) = b
1010278⟨a, b | aa=1, ababb=baa⟩φ(a) = a, φ(b) = b
1010513⟨a, b | aa=1, babb=aaab⟩φ(a) = a, φ(b) = b
1010516⟨a, b | aa=1, babb=abaa⟩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.

4 total

Σ#PresentationMapping
109705⟨a, b | aa=1, aabbaba=b⟩φ(a) = a, φ(b) = b
109976⟨a, b | aa=1, aabbab=ba⟩φ(a) = a, φ(b) = b
1010037⟨a, b | aa=1, baabab=ba⟩φ(a) = a, φ(b) = b
1010284⟨a, b | aa=1, abbab=aba⟩φ(a) = a, φ(b) = b