#7816 ⟨a, b | aaa=1, babbb=ba⟩

Up:Monoids with two generators and two relations
Prev:#7815 ⟨a, b | aaa=1, babbb=ab⟩
Next:#7817 ⟨a, b | aaa=1, babbb=bb⟩

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. a3 ⇒ 1
  2. b4 ⇒ b
  3. bab3 ⇒ ba
  4. ba2b3 ⇒ ba2 
# ab:aaa=1,babbb=ba ab
aaa=1
bbbb=b
babbb=ba
baabbb=baa

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other anti-isomorphic instances

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

2 total

Σ#PresentationMapping
1121703⟨a, b | aaa=1, aabbbab=b⟩φ(a) = a, φ(b) = b
1121743⟨a, b | aaa=1, abbbaab=b⟩φ(a) = a, φ(b) = b