#20295 ⟨a, b | aba=b, abbb=abb⟩

Up:Monoids with two generators and two relations
Prev:#20277 ⟨a, b | aba=b, aabb=bbb⟩
Next:#20297 ⟨a, b | aba=b, abbb=bab⟩

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 ⇒ b
  2. b2a ⇒ ab2
  3. a2b2 ⇒ b3
  4. ab3 ⇒ ab2
  5. bab2 ⇒ ab2
  6. b4 ⇒ b3 
# ab:aba=b,abbb=abb ab
aba=b
bba=abb
aabb=bbb
abbb=abb
babb=abb
bbbb=bbb

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.

3 total

Σ#PresentationMapping
1120298⟨a, b | aba=b, abbb=bba⟩φ(a) = a, φ(b) = b
1120309⟨a, b | aba=b, babb=abb⟩φ(a) = a, φ(b) = b
1120312⟨a, b | aba=b, babb=bba⟩φ(a) = a, φ(b) = b