#8883 ⟨a, b | aa=a, abbab=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. b2a ⇒ bab [7]
4. bab2 ⇒ ba [8]
# ab:aa=a,abbab=ba ab
aa=a
aba=ba
bba=bab
babb=ba

Isomorphic instances

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

4 total

Σ#PresentationMapping
1124636⟨a, b | aa=a, aabbab=ba⟩φ(a) = a, φ(b) = b
1124659⟨a, b | aa=a, ababab=ba⟩φ(a) = a, φ(b) = b
1124671⟨a, b | aa=a, abbaab=ba⟩φ(a) = a, φ(b) = b
1125202⟨a, b | aa=a, abbab=baa⟩φ(a) = a, φ(b) = b