#3244 ⟨a, b | ababababbba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

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
#RuleProof
1. dc ⇒ 1 [13]
2. cd ⇒ 1 [26]
3. cb ⇒ bc [5]
4. db ⇒ bd [23]
5. b3 ⇒ c [2]
6. a2b ⇒ bdaca [32]
7. acab2 ⇒ b2a2c [27]
8. a(ba)3c ⇒ (ba)3ca [6]
9. a(ba)2cad ⇒ b2da(ba)3 [36]
10. (ab)4c ⇒ (ba)3cab [31]
11. a(ba)2cabd ⇒ b2d(ab)4 [38]
12. (ab)4b ⇒ (ba)2ca2 [34]
13. a(ba)2ca2 ⇒ b2d [33]
14. ab(aca)2d ⇒ b2ab2da(ba)3 [40]
15. ab(aca)2bd ⇒ b2ab2d(ab)4 [42]
16. aba(ca2)2 ⇒ b2ab2d [29]
17. (aca)3d ⇒ b2(ab2)2da(ba)3 [43]
18. (aca)3bd ⇒ b2(ab2)2d(ab)4 [44]
19. a(ca2)3 ⇒ b2(ab2)2d [39]
# ab:ababababbba=1 reversed:cdb/a bbb=c,aabababa=d magic:1
dc=1
cd=1
cb=bc
db=bd
bbb=c
aab=bdaca
acabb=bbaac
abababac=bababaca
ababacad=bbdabababa
ababababc=bababacab
ababacabd=bbdabababab
ababababb=babacaa
ababacaa=bbd
abacaacad=bbabbdabababa
abacaacabd=bbabbdabababab
abacaacaa=bbabbd
acaacaacad=bbabbabbdabababa
acaacaacabd=bbabbabbdabababab
acaacaacaa=bbabbabbd

Isomorphic instances

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

1 total

Σ#PresentationMapping
113247⟨a, b | abababbbaab=1⟩φ(a) = a, φ(b) = b