#1800 ⟨a, b | abab=1, aaaaa=1⟩

Up:Monoids with two generators and two relations
Prev:#1789 ⟨a, b | aabb=1, aabab=1⟩
Next:#1803 ⟨a, b | abab=1, aaabb=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. a5 ⇒ 1
  2. bab ⇒ a4 
# ab:abab=1,aaaaa=1 a/b
aaaaa=1
bab=aaaa

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.

6 total

Σ#PresentationMapping
1110655⟨a, b | aaaa=bab, abab=1⟩φ(a) = a, φ(b) = b
1111537⟨a, b | ababb=b, bbbbb=1⟩φ(a) = b, φ(b) = a
1111615⟨a, b | babab=b, bbbbb=1⟩φ(a) = b, φ(b) = a
1117480⟨a, b | abab=1, aaaaaa=a⟩φ(a) = a, φ(b) = b
1117483⟨a, b | abab=1, aaaaab=b⟩φ(a) = a, φ(b) = b
1117529⟨a, b | abab=1, baaaaa=b⟩φ(a) = a, φ(b) = b