#2077 ⟨a, b | aab=b, bbaa=b⟩

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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. b2 ⇒ b [4]
2. a2b ⇒ b [1]
3. ba2 ⇒ b [5]
# ab:aab=b,bbaa=b ab
bb=b
aab=b
baa=b

Isomorphic instances

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

5 total

Σ#PresentationMapping
1112397⟨a, b | aaba=ba, bbaa=b⟩φ(a) = a, φ(b) = b
1118985⟨a, b | aab=b, aabbaa=b⟩φ(a) = a, φ(b) = b
1119033⟨a, b | aab=b, baabaa=b⟩φ(a) = a, φ(b) = b
1119553⟨a, b | aab=b, abbaa=ab⟩φ(a) = a, φ(b) = b
1120145⟨a, b | aab=b, bbaa=aab⟩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
1112446⟨a, b | aabb=aa, bbaa=a⟩φ(a) = b, φ(b) = a
1114713⟨a, b | aabb=a, bbaaa=a⟩φ(a) = b, φ(b) = a