#8808 ⟨a, b | ab=a, bbaaaa=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 ⇒ a [1]
2. b2a ⇒ a [6]
3. a4 ⇒ a [5]
# ab:ab=a,bbaaaa=a ab
ab=a
bba=a
aaaa=a

Isomorphic instances

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

9 total

Σ#PresentationMapping
1115720⟨a, b | aab=ba, babbb=b⟩φ(a) = b, φ(b) = a
1115728⟨a, b | aab=ba, bbabb=b⟩φ(a) = b, φ(b) = a
1115732⟨a, b | aab=ba, bbbab=b⟩φ(a) = b, φ(b) = a
1115734⟨a, b | aab=ba, bbbba=b⟩φ(a) = b, φ(b) = a
1124526⟨a, b | ab=a, bbaaaab=a⟩φ(a) = a, φ(b) = b
1124528⟨a, b | ab=a, bbaaaba=a⟩φ(a) = a, φ(b) = b
1124532⟨a, b | ab=a, bbaabaa=a⟩φ(a) = a, φ(b) = b
1124540⟨a, b | ab=a, bbabaaa=a⟩φ(a) = a, φ(b) = b
1125053⟨a, b | ab=a, bbaaaa=ab⟩φ(a) = a, φ(b) = b