#455 ⟨a, b | aaaa=1, aabb=1⟩

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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. b2 ⇒ a2 [3]
2. ba2 ⇒ a2b [4]
3. a4 ⇒ 1 [1]
# ab:aaaa=1,aabb=1 ab
bb=aa
baa=aab
aaaa=1

Isomorphic instances

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

23 total

Σ#PresentationMapping
8457⟨a, b | aaaa=1, abba=1⟩φ(a) = a, φ(b) = b
8459⟨a, b | aaaa=1, baab=1⟩φ(a) = a, φ(b) = b
8624⟨a, b | bb=aa, aaaa=1⟩φ(a) = a, φ(b) = b
8627⟨a, b | bb=aa, aabb=1⟩φ(a) = a, φ(b) = b
8629⟨a, b | bb=aa, abba=1⟩φ(a) = a, φ(b) = b
104038⟨a, b | abb=aaa, aaaa=1⟩φ(a) = a, φ(b) = b
104041⟨a, b | abb=aaa, aabb=1⟩φ(a) = a, φ(b) = b
104044⟨a, b | abb=aaa, abba=1⟩φ(a) = a, φ(b) = b
104047⟨a, b | abb=aaa, baab=1⟩φ(a) = a, φ(b) = b
104050⟨a, b | abb=aaa, bbaa=1⟩φ(a) = a, φ(b) = b
105700⟨a, b | aaaa=1, aaabb=a⟩φ(a) = a, φ(b) = b
105706⟨a, b | aaaa=1, aabba=a⟩φ(a) = a, φ(b) = b
105710⟨a, b | aaaa=1, abaab=a⟩φ(a) = a, φ(b) = b
105862⟨a, b | aabb=1, aaaaa=a⟩φ(a) = a, φ(b) = b
105865⟨a, b | aabb=1, aaaab=b⟩φ(a) = a, φ(b) = b
105871⟨a, b | aabb=1, aabaa=b⟩φ(a) = a, φ(b) = b
105887⟨a, b | aabb=1, baaaa=b⟩φ(a) = a, φ(b) = b
105926⟨a, b | abba=1, aaaaa=a⟩φ(a) = a, φ(b) = b
105929⟨a, b | abba=1, aaaab=b⟩φ(a) = a, φ(b) = b
105935⟨a, b | abba=1, aabaa=b⟩φ(a) = a, φ(b) = b
105952⟨a, b | abba=1, abbbb=a⟩φ(a) = a, φ(b) = b
105962⟨a, b | abba=1, bbabb=a⟩φ(a) = a, φ(b) = b
105965⟨a, b | abba=1, bbbbb=b⟩φ(a) = a, φ(b) = b