#4691 ⟨a, b | aaab=b, babb=a⟩

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Properties

Element profile

Complete 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
  1. b10 ⇒ b
  2. ab9 ⇒ a
  3. ba ⇒ ab7
  4. a3 ⇒ b9 
# ab:aaab=b,babb=a b/a
bbbbbbbbbb=b
abbbbbbbbb=a
ba=abbbbbbb
aaa=bbbbbbbbb

Right Cayley graph

Left Cayley graph

Others with same cardinality

2 unique, 5 total

Σ#PresentationDescriptionRelated
104623⟨a, b | aaaa=a, abba=b⟩Finite non-commutative monoid with 28 elements1 iso
104625⟨a, b | aaaa=a, abbb=b⟩Finite non-commutative monoid with 28 elements2 iso

Other isomorphic instances

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

3 total

Σ#PresentationMapping
104695⟨a, b | aaab=b, bbab=a⟩φ(a) = aa, φ(b) = b
104727⟨a, b | aaba=b, babb=a⟩φ(a) = b, φ(b) = aab
104730⟨a, b | aaba=b, bbab=a⟩φ(a) = b, φ(b) = aabb