#7 ⟨a, b | aa=b⟩

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Quick links

  1. Properties
  2. Staircase diagram
  3. Rewriting system
  4. Other submonoids of same group
  5. Isomorphic instances

Properties

Staircase diagram

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. b ⇒ a2 [1]
# ab:aa=b a/b
b=aa

Other submonoids of same group

1 unique, 68 total

Σ#PresentationDescriptionRelated
35⟨a, b | aba=1⟩Isomorphic to ℤ67 iso

Isomorphic instances

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

8 total

Σ#PresentationMapping
416⟨a, b | aaa=b⟩φ(a) = a, φ(b) = aaa
535⟨a, b | aaaa=b⟩φ(a) = a, φ(b) = aaaa
675⟨a, b | aaaaa=b⟩φ(a) = a, φ(b) = aaaaa
7162⟨a, b | aaaaaa=b⟩φ(a) = a, φ(b) = aaaaaa
8342⟨a, b | aaaaaaa=b⟩φ(a) = a, φ(b) = aaaaaaa
9732⟨a, b | aaaaaaaa=b⟩φ(a) = a, φ(b) = aaaaaaaa
101548⟨a, b | aaaaaaaaa=b⟩φ(a) = a, φ(b) = aaaaaaaaa
113306⟨a, b | aaaaaaaaaa=b⟩φ(a) = a, φ(b) = aaaaaaaaaa