#6950 ⟨a, b | ab=aa, aaaaa=a⟩

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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. a5 ⇒ a [2]
# ab:ab=aa,aaaaa=a ab
ab=aa
aaaaa=a

Isomorphic instances

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

15 total

Σ#PresentationMapping
106952⟨a, b | ab=aa, aaaab=a⟩φ(a) = a, φ(b) = b
106954⟨a, b | ab=aa, aaaba=a⟩φ(a) = a, φ(b) = b
106956⟨a, b | ab=aa, aaabb=a⟩φ(a) = a, φ(b) = b
106958⟨a, b | ab=aa, aabaa=a⟩φ(a) = a, φ(b) = b
106960⟨a, b | ab=aa, aabab=a⟩φ(a) = a, φ(b) = b
106962⟨a, b | ab=aa, aabba=a⟩φ(a) = a, φ(b) = b
106964⟨a, b | ab=aa, aabbb=a⟩φ(a) = a, φ(b) = b
106966⟨a, b | ab=aa, abaaa=a⟩φ(a) = a, φ(b) = b
106968⟨a, b | ab=aa, abaab=a⟩φ(a) = a, φ(b) = b
106970⟨a, b | ab=aa, ababa=a⟩φ(a) = a, φ(b) = b
106972⟨a, b | ab=aa, ababb=a⟩φ(a) = a, φ(b) = b
106974⟨a, b | ab=aa, abbaa=a⟩φ(a) = a, φ(b) = b
106976⟨a, b | ab=aa, abbab=a⟩φ(a) = a, φ(b) = b
106978⟨a, b | ab=aa, abbba=a⟩φ(a) = a, φ(b) = b
106980⟨a, b | ab=aa, abbbb=a⟩φ(a) = a, φ(b) = b