#11590 ⟨a, b | baaab=a, bbbbb=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. ac ⇒ ca
  2. c2a2 ⇒ c
  3. ca3 ⇒ a
  4. cbca2 ⇒ cb
  5. abca2 ⇒ ab
  6. c2b ⇒ bc2
  7. a2b ⇒ cba4
  8. c2ab ⇒ abc2
  9. bcab ⇒ c2a
  10. cb2ca2 ⇒ cb2
  11. ab2ca2 ⇒ ab2
  12. b3c ⇒ cabcba5
  13. b3a ⇒ cabcba8
  14. b(cb)2 ⇒ ab2c6a
  15. cb3 ⇒ abcba3
  16. ab3 ⇒ bcba7
  17. (ab2)2 ⇒ (bcba)2a14
  18. (abcb)2 ⇒ cb2ab2c6a
  19. b5 ⇒ 1 
# ab:baaab=a,bbbbb=1 ca/b baabaabaabaab=c frequency:13/0
ac=ca
ccaa=c
caaa=a
cbcaa=cb
abcaa=ab
ccb=bcc
aab=cbaaaa
ccab=abcc
bcab=cca
cbbcaa=cbb
abbcaa=abb
bbbc=cabcbaaaaa
bbba=cabcbaaaaaaaa
bcbcb=abbcccccca
cbbb=abcbaaa
abbb=bcbaaaaaaa
abbabb=bcbabcbaaaaaaaaaaaaaaa
abcbabcb=cbbabbcccccca
bbbbb=1

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
1112859⟨a, b | bab=aaa, bbbbb=1⟩φ(a) = a, φ(b) = bbbb