#1803 ⟨a, b | abab=1, aaabb=1⟩

Up:Monoids with two generators and two relations
Prev:#1800 ⟨a, b | abab=1, aaaaa=1⟩
Next:#1855 ⟨a, b | aaa=a, bbbbb=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. (ab)2 ⇒ 1
  2. a3b2 ⇒ 1 
# ab:abab=1,aaabb=1 ab
abab=1
aaabb=1

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.

2 total

Σ#PresentationMapping
1111512⟨a, b | ababa=a, bbbaa=1⟩φ(a) = b, φ(b) = a
1117492⟨a, b | abab=1, aaabba=a⟩φ(a) = a, φ(b) = b