#1414 ⟨a, b | aabaabbbba=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 [10]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [9]
5. a3 ⇒ c [2]
6. ba2ba ⇒ d(bc)2 [20]
7. bcba2 ⇒ cba2b [18]
8. ba2b2a ⇒ db(bc)2 [25]
9. b(cba)2 ⇒ cba2d(bc)2 [24]
10. b4c ⇒ aba2b3 [14]
11. ba2b3d ⇒ a2db4 [11]
12. b4a ⇒ adb3cb [31]
13. ba2b3a ⇒ db3cbc [28]
14. bcbacb2a ⇒ cba2db(bc)2 [27]
15. ba2b4 ⇒ d [3]
16. bcbacb3d ⇒ cbab4 [23]
17. bcbacb3a ⇒ cba2db3cbc [37]
18. b3c(ba)2 ⇒ a2b3d(bc)2 [38]
19. bcbacb4 ⇒ cba2d [22]
20. b3cbab2a ⇒ a2b3db(bc)2 [39]
21. b3cbab3d ⇒ a2b3a2db4 [41]
22. b3cbab3a ⇒ a2b3db3cbc [40]
23. b3cbab4 ⇒ a2b3d [30]
# ab:aabaabbbba=1 reversed:cda/b aaa=c,baabbbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
baaba=dbcbc
bcbaa=cbaab
baabba=dbbcbc
bcbacba=cbaadbcbc
bbbbc=abaabbb
baabbbd=aadbbbb
bbbba=adbbbcb
baabbba=dbbbcbc
bcbacbba=cbaadbbcbc
baabbbb=d
bcbacbbbd=cbabbbb
bcbacbbba=cbaadbbbcbc
bbbcbaba=aabbbdbcbc
bcbacbbbb=cbaad
bbbcbabba=aabbbdbbcbc
bbbcbabbbd=aabbbaadbbbb
bbbcbabbba=aabbbdbbbcbc
bbbcbabbbb=aabbbd

Isomorphic instances

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

1 total

Σ#PresentationMapping
101466⟨a, b | aabbbbaaab=1⟩φ(a) = a, φ(b) = b