#14584 ⟨a, b | aaba=a, babbb=b⟩

Up:Monoids with two generators and two relations
Prev:#14580 ⟨a, b | aaba=a, babab=b⟩
Next:#14585 ⟨a, b | aaba=a, bbaaa=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. bab3 ⇒ b
  2. b2ab ⇒ bab2
  3. a2b ⇒ ab3
  4. ab3a ⇒ a
  5. ab5a ⇒ a2
  6. ba2 ⇒ b3a
  7. a3 ⇒ ab7a 
# ab:aaba=a,babbb=b b/a
babbb=b
bbab=babb
aab=abbb
abbba=a
abbbbba=aa
baa=bbba
aaa=abbbbbbba

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
1114592⟨a, b | aaba=a, bbabb=b⟩φ(a) = a, φ(b) = b
1114822⟨a, b | abba=a, baaab=b⟩φ(a) = b, φ(b) = a