#19558 ⟨a, b | aab=b, abbab=ba⟩

Up:Monoids with two generators and two relations
Prev:#19555 ⟨a, b | aab=b, abbaa=bb⟩
Next:#19559 ⟨a, b | aab=b, abbab=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. b6 ⇒ b2
  2. bab4 ⇒ ba
  3. b4a ⇒ ab4
  4. a2b ⇒ b
  5. aba ⇒ b2ab
  6. ab2a ⇒ bab3
  7. ab3a ⇒ b3ab2
  8. ba2 ⇒ b5 
# ab:aab=b,abbab=ba b/a
bbbbbb=bb
babbbb=ba
bbbba=abbbb
aab=b
aba=bbab
abba=babbb
abbba=bbbabb
baa=bbbbb

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
1120154⟨a, b | aab=b, bbab=aba⟩φ(a) = a, φ(b) = b