#7054 ⟨a, b | ab=aa, aaaa=aa⟩

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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. ab ⇒ a2 [1]
2. a4 ⇒ a2 [2]
# ab:ab=aa,aaaa=aa ab
ab=aa
aaaa=aa

Isomorphic instances

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

15 total

Σ#PresentationMapping
107055⟨a, b | ab=aa, aaaa=ab⟩φ(a) = a, φ(b) = b
107058⟨a, b | ab=aa, aaab=aa⟩φ(a) = a, φ(b) = b
107059⟨a, b | ab=aa, aaab=ab⟩φ(a) = a, φ(b) = b
107062⟨a, b | ab=aa, aaba=aa⟩φ(a) = a, φ(b) = b
107063⟨a, b | ab=aa, aaba=ab⟩φ(a) = a, φ(b) = b
107066⟨a, b | ab=aa, aabb=aa⟩φ(a) = a, φ(b) = b
107067⟨a, b | ab=aa, aabb=ab⟩φ(a) = a, φ(b) = b
107070⟨a, b | ab=aa, abaa=aa⟩φ(a) = a, φ(b) = b
107071⟨a, b | ab=aa, abaa=ab⟩φ(a) = a, φ(b) = b
107074⟨a, b | ab=aa, abab=aa⟩φ(a) = a, φ(b) = b
107075⟨a, b | ab=aa, abab=ab⟩φ(a) = a, φ(b) = b
107078⟨a, b | ab=aa, abba=aa⟩φ(a) = a, φ(b) = b
107079⟨a, b | ab=aa, abba=ab⟩φ(a) = a, φ(b) = b
107082⟨a, b | ab=aa, abbb=aa⟩φ(a) = a, φ(b) = b
107083⟨a, b | ab=aa, abbb=ab⟩φ(a) = a, φ(b) = b