#2048 ⟨a, b | aab=a, bbba=a⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-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. a4 ⇒ a [5]
2. ab ⇒ a3 [6]
3. b3a ⇒ a [2]
# ab:aab=a,bbba=a a/b
aaaa=a
ab=aaa
bbba=a

Isomorphic instances

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

6 total

Σ#PresentationMapping
1118946⟨a, b | aab=a, bbbaab=a⟩φ(a) = a, φ(b) = b
1118948⟨a, b | aab=a, bbbaba=a⟩φ(a) = a, φ(b) = b
1119488⟨a, b | aab=a, bbbaa=aa⟩φ(a) = a, φ(b) = b
1119493⟨a, b | aab=a, bbbab=ab⟩φ(a) = a, φ(b) = b
1120033⟨a, b | aab=a, bbba=aab⟩φ(a) = a, φ(b) = b
1120034⟨a, b | aab=a, bbba=aba⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

2 total

Σ#PresentationMapping
1112587⟨a, b | abba=ba, baaa=b⟩φ(a) = b, φ(b) = a
1119146⟨a, b | aba=a, baabbb=a⟩φ(a) = a, φ(b) = b