#1360 ⟨a, b | aaababbaba=1⟩

Up:Monoids with two generators and one relation
Prev:#1359 ⟨a, b | aaababbaab=1⟩
Next:#1361 ⟨a, b | aaababbabb=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. ca ⇒ ac
  2. a4 ⇒ c
  3. dc ⇒ 1
  4. dac ⇒ a
  5. da2c ⇒ a2
  6. da3c ⇒ a3
  7. ad ⇒ da
  8. cd ⇒ 1
  9. cbab ⇒ babc
  10. dbab ⇒ babd
  11. d(ab)2 ⇒ (ab)2d
  12. da(ab)2 ⇒ a(ab)2d
  13. da3bab ⇒ a3babd
  14. ab2ab ⇒ babcbda
  15. acb2ab ⇒ babc2bda
  16. a3bab2 ⇒ b2aba3
  17. a3babcb ⇒ cb2aba3
  18. a3babc2b ⇒ c2b2aba3
  19. ac2b2ab ⇒ babc3bda
  20. c3b2ab ⇒ a3babc3bda
  21. db2ab ⇒ a3ba(bd)2a
  22. b2abcb ⇒ da3 
# ab:aaababbaba=1 ac/d/b aaaa=c,babbab=d magic:0
ca=ac
aaaa=c
dc=1
dac=a
daac=aa
daaac=aaa
ad=da
cd=1
cbab=babc
dbab=babd
dabab=ababd
daabab=aababd
daaabab=aaababd
abbab=babcbda
acbbab=babccbda
aaababb=bbabaaa
aaababcb=cbbabaaa
aaababccb=ccbbabaaa
accbbab=babcccbda
cccbbab=aaababcccbda
dbbab=aaababdbda
bbabcb=daaa

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
101429⟨a, b | aababbabaa=1⟩φ(a) = a, φ(b) = b
101535⟨a, b | abbabaaaab=1⟩φ(a) = a, φ(b) = b