#5338 ⟨a, b | aaa=bb, aab=aa⟩

Up:Monoids with two generators and two relations
Prev:#5337 ⟨a, b | aaa=ab, bbb=ba⟩
Next:#5339 ⟨a, b | aaa=bb, aab=ab⟩

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. a5 ⇒ a2
  2. ba2 ⇒ a2
  3. a2b ⇒ a2
  4. b2 ⇒ a3 
# ab:aaa=bb,aab=aa a/b
aaaaa=aa
baa=aa
aab=aa
bb=aaa

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.

2 total

Σ#PresentationMapping
1116088⟨a, b | aab=aa, aaab=bb⟩φ(a) = a, φ(b) = b
1116092⟨a, b | aab=aa, aaba=bb⟩φ(a) = a, φ(b) = b