#1439 ⟨a, b | aabbaaaabb=1⟩

Up:Monoids with two generators and one relation
Prev:#1437 ⟨a, b | aabbaaaaab=1⟩
Next:#1440 ⟨a, b | aabbaaabab=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. b2 ⇒ c
  2. cb ⇒ bc
  3. cd ⇒ 1
  4. db ⇒ bd
  5. dc ⇒ 1
  6. da ⇒ cad2
  7. c2a ⇒ ac2
  8. ca2 ⇒ a2c
  9. a6 ⇒ d2 
# ab:aabbaaaabb=1 bcd/a bb=c,aaaabbaa=d magic:1
bb=c
cb=bc
cd=1
db=bd
dc=1
da=cadd
cca=acc
caa=aac
aaaaaa=dd

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
101528⟨a, b | abbaaaabba=1⟩φ(a) = a, φ(b) = b