#16059 ⟨a, b | aaa=bb, aabb=bb⟩

Up:Monoids with two generators and two relations
Prev:#16057 ⟨a, b | aaa=bb, aabb=ab⟩
Next:#16060 ⟨a, b | aaa=bb, abab=aa⟩

Properties

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. b6 ⇒ b2
  2. ab2 ⇒ b4
  3. b2a ⇒ b4
  4. a3 ⇒ b2 
# ab:aaa=bb,aabb=bb b/a
bbbbbb=bb
abb=bbbb
bba=bbbb
aaa=bb

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

1 total

Σ#PresentationMapping
1116066⟨a, b | aaa=bb, abba=bb⟩φ(a) = a, φ(b) = b