#664 ⟨a, b | aabaabbba=1⟩

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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. cd ⇒ 1
  2. dc ⇒ 1
  3. ac ⇒ ca
  4. ad ⇒ da
  5. a3 ⇒ c
  6. cba2b ⇒ bcba2
  7. dbcb ⇒ ba2bda
  8. caba2b ⇒ abcba2
  9. dabcb ⇒ aba2bda
  10. c(a2b)2 ⇒ a2bcba2
  11. da2bcb ⇒ (a2b)2da
  12. db2cb ⇒ ba2b2da
  13. ab2cb ⇒ cb3a
  14. aba2b2 ⇒ b3c
  15. a2b3 ⇒ b2cbda2
  16. b3cb ⇒ da
  17. cbab3 ⇒ (bc)2ab2d
  18. cbcab3 ⇒ b(bc)2a2bda2
  19. abcab3 ⇒ b3c2bda2
  20. cabab3 ⇒ a(bc)2ab2d
  21. ca2bab3 ⇒ a2(bc)2ab2d 
# ab:aabaabbba=1 cda/b aaa=c,baabbb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
cbaab=bcbaa
dbcb=baabda
cabaab=abcbaa
dabcb=abaabda
caabaab=aabcbaa
daabcb=aabaabda
dbbcb=baabbda
abbcb=cbbba
abaabb=bbbc
aabbb=bbcbdaa
bbbcb=da
cbabbb=bcbcabbd
cbcabbb=bbcbcaabdaa
abcabbb=bbbccbdaa
cababbb=abcbcabbd
caababbb=aabcbcabbd

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other anti-isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

2 total

Σ#PresentationMapping
9687⟨a, b | aabbbaaba=1⟩φ(a) = a, φ(b) = b
9702⟨a, b | abaaabbba=1⟩φ(a) = a, φ(b) = b