#27687 ⟨a, b | aa=1, abbbba=bbb⟩

Up:Monoids with two generators and two relations
Prev:#27686 ⟨a, b | aa=1, abbbba=bab⟩
Next:#27693 ⟨a, b | aa=1, abbbbb=bab⟩

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. b10 ⇒ b3
  2. bab3 ⇒ ab9
  3. b3a ⇒ ab4
  4. a2 ⇒ 1 
# ab:aa=1,abbbba=bbb b/a
bbbbbbbbbb=bbb
babbb=abbbbbbbbb
bbba=abbbb
aa=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
1128207⟨a, b | aa=1, abbba=bbbb⟩φ(a) = a, φ(b) = b
1128222⟨a, b | aa=1, abbbb=bbba⟩φ(a) = a, φ(b) = b