#20616 ⟨a, b | ab=aa, bbaaaa=a⟩

Up:Monoids with two generators and two relations
Prev:#20584 ⟨a, b | ab=aa, baaaaa=a⟩
Next:#20632 ⟨a, b | ab=aa, bbbaaa=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. a6 ⇒ a 
# ab:ab=aa,bbaaaa=a ab
ab=aa
bba=aaa
aaaaaa=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.

7 total

Σ#PresentationMapping
1120618⟨a, b | ab=aa, bbaaab=a⟩φ(a) = a, φ(b) = b
1120620⟨a, b | ab=aa, bbaaba=a⟩φ(a) = a, φ(b) = b
1120622⟨a, b | ab=aa, bbaabb=a⟩φ(a) = a, φ(b) = b
1120624⟨a, b | ab=aa, bbabaa=a⟩φ(a) = a, φ(b) = b
1120626⟨a, b | ab=aa, bbabab=a⟩φ(a) = a, φ(b) = b
1120628⟨a, b | ab=aa, bbabba=a⟩φ(a) = a, φ(b) = b
1120630⟨a, b | ab=aa, bbabbb=a⟩φ(a) = a, φ(b) = b