#20722 ⟨a, b | ab=aa, aaaaa=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. a6 ⇒ a3 [3]
2. ba ⇒ a5 [2]
3. ab ⇒ a2 [1]
# ab:ab=aa,aaaaa=ba a/b
aaaaaa=aaa
ba=aaaaa
ab=aa

Isomorphic instances

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

15 total

Σ#PresentationMapping
1120726⟨a, b | ab=aa, aaaab=ba⟩φ(a) = a, φ(b) = b
1120730⟨a, b | ab=aa, aaaba=ba⟩φ(a) = a, φ(b) = b
1120734⟨a, b | ab=aa, aaabb=ba⟩φ(a) = a, φ(b) = b
1120738⟨a, b | ab=aa, aabaa=ba⟩φ(a) = a, φ(b) = b
1120742⟨a, b | ab=aa, aabab=ba⟩φ(a) = a, φ(b) = b
1120746⟨a, b | ab=aa, aabba=ba⟩φ(a) = a, φ(b) = b
1120750⟨a, b | ab=aa, aabbb=ba⟩φ(a) = a, φ(b) = b
1120754⟨a, b | ab=aa, abaaa=ba⟩φ(a) = a, φ(b) = b
1120758⟨a, b | ab=aa, abaab=ba⟩φ(a) = a, φ(b) = b
1120762⟨a, b | ab=aa, ababa=ba⟩φ(a) = a, φ(b) = b
1120766⟨a, b | ab=aa, ababb=ba⟩φ(a) = a, φ(b) = b
1120770⟨a, b | ab=aa, abbaa=ba⟩φ(a) = a, φ(b) = b
1120774⟨a, b | ab=aa, abbab=ba⟩φ(a) = a, φ(b) = b
1120778⟨a, b | ab=aa, abbba=ba⟩φ(a) = a, φ(b) = b
1120782⟨a, b | ab=aa, abbbb=ba⟩φ(a) = a, φ(b) = b