#485 ⟨a, b | aabb=1, abba=1⟩

Up:Monoids with two generators and two relations
Prev:#484 ⟨a, b | aabb=1, abab=1⟩
Next:#486 ⟨a, b | aabb=1, baba=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. ac ⇒ ca
  2. bc ⇒ cb
  3. b2 ⇒ c
  4. ca2 ⇒ 1
  5. ba2 ⇒ a2b 
# ab:aabb=1,abba=1 cab bb=c frequency:2/0
ac=ca
bc=cb
bb=c
caa=1
baa=aab

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.

14 total

Σ#PresentationMapping
8487⟨a, b | aabb=1, bbaa=1⟩φ(a) = a, φ(b) = b
8490⟨a, b | abba=1, baab=1⟩φ(a) = a, φ(b) = b
104083⟨a, b | baa=aab, aabb=1⟩φ(a) = a, φ(b) = b
104085⟨a, b | baa=aab, abba=1⟩φ(a) = a, φ(b) = b
104087⟨a, b | baa=aab, baab=1⟩φ(a) = a, φ(b) = b
105882⟨a, b | aabb=1, abbaa=a⟩φ(a) = a, φ(b) = b
105888⟨a, b | aabb=1, baaba=a⟩φ(a) = a, φ(b) = b
105892⟨a, b | aabb=1, bbaaa=a⟩φ(a) = a, φ(b) = b
105932⟨a, b | abba=1, aaabb=a⟩φ(a) = a, φ(b) = b
105938⟨a, b | abba=1, aabba=a⟩φ(a) = a, φ(b) = b
105941⟨a, b | abba=1, aabbb=b⟩φ(a) = a, φ(b) = b
105942⟨a, b | abba=1, abaab=a⟩φ(a) = a, φ(b) = b
105949⟨a, b | abba=1, abbab=b⟩φ(a) = a, φ(b) = b
105957⟨a, b | abba=1, baabb=b⟩φ(a) = a, φ(b) = b