#7542 ⟨a, b | aaa=1, babbab=a⟩

Up:Monoids with two generators and two relations
Prev:#7541 ⟨a, b | aaa=1, bababb=b⟩
Next:#7543 ⟨a, b | aaa=1, babbab=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. c4 ⇒ 1
  2. c2b ⇒ bc2
  3. c2a ⇒ ac2
  4. bcb ⇒ cac2
  5. ba ⇒ c
  6. acb ⇒ c2
  7. a2 ⇒ cbc2 
# ab:aaa=1,babbab=a c/ba ba=c frequency:2/1
cccc=1
ccb=bcc
cca=acc
bcb=cacc
ba=c
acb=cc
aa=cbcc

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
1121196⟨a, b | aaa=1, ababbaba=1⟩φ(a) = a, φ(b) = b