#2200 ⟨a, b | ab=aa, bbaa=a⟩

Up:Monoids with two generators and two relations
Prev:#2192 ⟨a, b | ab=aa, baaa=a⟩
Next:#2204 ⟨a, b | ab=aa, bbba=a⟩

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. ab ⇒ a2
  2. b2a ⇒ a3
  3. a4 ⇒ a 
# ab:ab=aa,bbaa=a ab
ab=aa
bba=aaa
aaaa=a

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.

10 total

Σ#PresentationMapping
92202⟨a, b | ab=aa, bbab=a⟩φ(a) = a, φ(b) = b
104669⟨a, b | aaab=a, bbaa=a⟩φ(a) = a, φ(b) = b
104717⟨a, b | aaba=b, aabb=b⟩φ(a) = b, φ(b) = a
104724⟨a, b | aaba=b, baab=b⟩φ(a) = b, φ(b) = a
104726⟨a, b | aaba=b, baba=b⟩φ(a) = b, φ(b) = a
104729⟨a, b | aaba=b, bbaa=b⟩φ(a) = b, φ(b) = a
1112904⟨a, b | aab=aaa, bbaa=a⟩φ(a) = a, φ(b) = b
1113017⟨a, b | abb=aba, aaba=b⟩φ(a) = b, φ(b) = a
1113019⟨a, b | abb=aba, aabb=b⟩φ(a) = b, φ(b) = a
1113038⟨a, b | abb=aba, bbab=a⟩φ(a) = a, φ(b) = b