#2946 ⟨a, b | aaababbabba=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. cd ⇒ 1 [30]
2. dc ⇒ 1 [20]
3. bc ⇒ cb [5]
4. bd ⇒ db [29]
5. b2 ⇒ c [2]
6. ba(ca)2 ⇒ ab(ac)2 [37]
7. (ba)2ca ⇒ (ca)3d [36]
8. ca4 ⇒ a3bab [42]
9. da3ba ⇒ a4db [41]
10. ba2baca ⇒ (ca)3ad [46]
11. cba4 ⇒ ba3bab [43]
12. dba3ba ⇒ ba4db [44]
13. ba4ba ⇒ (ac)2a3d [48]
14. ba3baca ⇒ (ca)3a2d [51]
15. a4baca ⇒ d [18]
16. da3(ca)3 ⇒ a5cac [53]
17. ba(ac)2a3 ⇒ (ca)3da3b [56]
18. dba3(ca)3 ⇒ ba5cac [54]
19. ba4(ca)3 ⇒ (ac)2a3db(ac)2 [58]
20. ba3caca3 ⇒ (ca)3ada3b [57]
21. da4caca3 ⇒ (a4b)2 [49]
22. ba4caca3 ⇒ (ca)3a2da3b [59]
23. c(ca)3a2da3 ⇒ ba3(bac)2a3db [62]
24. a5caca3 ⇒ da3b [55]
# ab:aaababbabba=1 cdb/a bb=c,abbaaaaba=d magic:1
cd=1
dc=1
bc=cb
bd=db
bb=c
bacaca=abacac
babaca=cacacad
caaaa=aaabab
daaaba=aaaadb
baabaca=cacacaad
cbaaaa=baaabab
dbaaaba=baaaadb
baaaaba=acacaaad
baaabaca=cacacaaad
aaaabaca=d
daaacacaca=aaaaacac
baacacaaa=cacacadaaab
dbaaacacaca=baaaaacac
baaaacacaca=acacaaadbacac
baaacacaaa=cacacaadaaab
daaaacacaaa=aaaabaaaab
baaaacacaaa=cacacaaadaaab
ccacacaaadaaa=baaabacbacaaadb
aaaaacacaaa=daaab

Isomorphic instances

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

4 total

Σ#PresentationMapping
113081⟨a, b | aababbabbaa=1⟩φ(a) = a, φ(b) = b
113156⟨a, b | aabbbbabaab=1⟩φ(a) = b, φ(b) = a
113225⟨a, b | abaabbbbaba=1⟩φ(a) = b, φ(b) = a
113290⟨a, b | abbabbaaaab=1⟩φ(a) = a, φ(b) = b