#1623 ⟨a, b | aaababaaa=a⟩

Up:Monoids with two generators and one relation
Prev:#1622 ⟨a, b | aaabaabbb=b⟩
Next:#1624 ⟨a, b | aaababaaa=b⟩

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. aba ⇒ c
  2. cba ⇒ abc
  3. a2bc ⇒ abca
  4. acbc ⇒ abc2
  5. cabc ⇒ cbca
  6. c2bc ⇒ cbc2
  7. ca4 ⇒ a4c
  8. ca3c ⇒ a 
# ab:aaababaaa=a bac aba=c frequency:3/0
aba=c
cba=abc
aabc=abca
acbc=abcc
cabc=cbca
ccbc=cbcc
caaaa=aaaac
caaac=a

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.

1 total

Σ#PresentationMapping
101749⟨a, b | abaaaaaba=a⟩φ(a) = a, φ(b) = b