#3020 ⟨a, b | aa=a, abba=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. ab2 ⇒ ab [4]
# ab:aa=a,abba=ab ab
aa=a
aba=ab
abb=ab

Isomorphic instances

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

10 total

Σ#PresentationMapping
108863⟨a, b | aa=a, aabba=ab⟩φ(a) = a, φ(b) = b
108875⟨a, b | aa=a, ababa=ab⟩φ(a) = a, φ(b) = b
109151⟨a, b | aa=a, abba=aab⟩φ(a) = a, φ(b) = b
1124612⟨a, b | aa=a, aaabba=ab⟩φ(a) = a, φ(b) = b
1124624⟨a, b | aa=a, aababa=ab⟩φ(a) = a, φ(b) = b
1124632⟨a, b | aa=a, aabbaa=ab⟩φ(a) = a, φ(b) = b
1124651⟨a, b | aa=a, abaaba=ab⟩φ(a) = a, φ(b) = b
1125161⟨a, b | aa=a, aabba=aab⟩φ(a) = a, φ(b) = b
1125185⟨a, b | aa=a, ababa=aab⟩φ(a) = a, φ(b) = b
1125675⟨a, b | aa=a, abba=aaab⟩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
108864⟨a, b | aa=a, aabba=ba⟩φ(a) = a, φ(b) = b
1124613⟨a, b | aa=a, aaabba=ba⟩φ(a) = a, φ(b) = b
1124625⟨a, b | aa=a, aababa=ba⟩φ(a) = a, φ(b) = b
1125164⟨a, b | aa=a, aabba=baa⟩φ(a) = a, φ(b) = b