#3016 ⟨a, b | aa=a, abab=ab⟩

Up:Monoids with two generators and two relations
Prev:#3009 ⟨a, b | aa=a, aaba=ba⟩
Next:#3017 ⟨a, b | aa=a, abab=ba⟩

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. a2 ⇒ a
  2. (ab)2 ⇒ ab 
# ab:aa=a,abab=ab ab
aa=a
abab=ab

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.

9 total

Σ#PresentationMapping
108859⟨a, b | aa=a, aabab=ab⟩φ(a) = a, φ(b) = b
108871⟨a, b | aa=a, abaab=ab⟩φ(a) = a, φ(b) = b
109143⟨a, b | aa=a, abab=aab⟩φ(a) = a, φ(b) = b
1124608⟨a, b | aa=a, aaabab=ab⟩φ(a) = a, φ(b) = b
1124620⟨a, b | aa=a, aabaab=ab⟩φ(a) = a, φ(b) = b
1124647⟨a, b | aa=a, abaaab=ab⟩φ(a) = a, φ(b) = b
1125153⟨a, b | aa=a, aabab=aab⟩φ(a) = a, φ(b) = b
1125177⟨a, b | aa=a, abaab=aab⟩φ(a) = a, φ(b) = b
1125670⟨a, b | aa=a, abab=aaab⟩φ(a) = a, φ(b) = b