#4917 ⟨a, b | aab=ba, bbbbb=1⟩

Up:Monoids with two generators and two relations
Prev:#4886 ⟨a, b | aab=ba, aaaaa=1⟩
Next:#4969 ⟨a, b | aba=aa, bbbbb=1⟩

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. a32 ⇒ a
  2. ba ⇒ a2b
  3. b5 ⇒ 1 
# ab:aab=ba,bbbbb=1 reversed:a/b
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa=a
ba=aab
bbbbb=1

Right Cayley graph

Left Cayley graph

Other isomorphic instances

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

1 total

Σ#PresentationMapping
1112060⟨a, b | abab=ba, aaaaa=1⟩φ(a) = bbbb, φ(b) = ab