#1288 ⟨a, b | aba=aab, bbb=1⟩

Up:Monoids with two generators and two relations
Prev:#1284 ⟨a, b | aba=aab, abb=1⟩
Next:#1302 ⟨a, b | baa=aab, bbb=1⟩

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. aba ⇒ a2b
  2. b3 ⇒ 1
  3. a2b2a ⇒ a3b2 
# ab:aba=aab,bbb=1 ab
aba=aab
bbb=1
aabba=aaabb

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
1123282⟨a, b | aaa=1, abba=abab⟩φ(a) = b, φ(b) = a