#282 ⟨a, b | ab=b, bb=ab⟩

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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 ⇒ b [1]
2. b2 ⇒ b [2]
# ab:ab=b,bb=ab ab
ab=b
bb=b

Isomorphic instances

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

10 total

Σ#PresentationMapping
91625⟨a, b | aab=ab, abb=b⟩φ(a) = a, φ(b) = b
105133⟨a, b | aab=ab, aabb=b⟩φ(a) = a, φ(b) = b
105137⟨a, b | aab=ab, abab=b⟩φ(a) = a, φ(b) = b
1112460⟨a, b | aabb=ab, abbb=b⟩φ(a) = a, φ(b) = b
1112521⟨a, b | abab=ab, abbb=b⟩φ(a) = a, φ(b) = b
1112619⟨a, b | baab=ab, babb=b⟩φ(a) = a, φ(b) = b
1112621⟨a, b | baab=ab, bbab=b⟩φ(a) = a, φ(b) = b
1115616⟨a, b | aab=ab, aaabb=b⟩φ(a) = a, φ(b) = b
1115620⟨a, b | aab=ab, aabab=b⟩φ(a) = a, φ(b) = b
1115628⟨a, b | aab=ab, abaab=b⟩φ(a) = a, φ(b) = b