#4107 ⟨a, b | bab=aaa, bbbb=1⟩

Up:Monoids with two generators and two relations
Prev:#4095 ⟨a, b | baa=abb, abab=1⟩
Next:#4118 ⟨a, b | bbb=aaa, abab=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. ad ⇒ da
  2. d2a2 ⇒ d
  3. da3 ⇒ a
  4. dcda2 ⇒ dc
  5. acda2 ⇒ ac
  6. d2c ⇒ cd2
  7. a2c ⇒ dca4
  8. d2ac ⇒ acd2
  9. cdac ⇒ d2a
  10. dc2da2 ⇒ dc2
  11. ac2 ⇒ cdca7
  12. acdc ⇒ dc2d2a
  13. c3d ⇒ daca
  14. c3a ⇒ daca4
  15. c(dc)2 ⇒ acd6a
  16. dc3 ⇒ acda
  17. c4 ⇒ 1
  18. b ⇒ c3 
# ab:bab=aaa,bbbb=1 da/c/b bbb=c,caacaacaac=d frequency:3/2,10/0
ad=da
ddaa=d
daaa=a
dcdaa=dc
acdaa=ac
ddc=cdd
aac=dcaaaa
ddac=acdd
cdac=dda
dccdaa=dcc
acc=cdcaaaaaaa
acdc=dccdda
cccd=daca
ccca=dacaaaa
cdcdc=acdddddda
dccc=acda
cccc=1
b=ccc

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
105719⟨a, b | aaaa=1, abbba=b⟩φ(a) = c, φ(b) = a