#3161 ⟨a, b | aabbbbbaaba=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. ba2bc ⇒ a2bcb [26]
7. bcbd ⇒ adba2b [40]
8. ba2bac ⇒ a2bcba [36]
9. bcbad ⇒ adba2ba [31]
10. (ba2)2c ⇒ a2bcba2 [41]
11. bcba2d ⇒ ad(ba2)2 [42]
12. bcb2d ⇒ adb2a2b [45]
13. bcb2ad ⇒ adb2a2ba [32]
14. bcb2a2d ⇒ adb(ba2)2 [46]
15. bcb3d ⇒ adb3a2b [48]
16. bcb3ad ⇒ adb3a2ba [33]
17. bcb3a2d ⇒ adb2(ba2)2 [50]
18. bcb4d ⇒ adb4a2b [52]
19. bcb4a ⇒ ab5c [49]
20. b4a2ba ⇒ cb5 [18]
21. b5a2 ⇒ a2dbcb4 [29]
22. bcb5 ⇒ ad [28]
23. b5abc ⇒ db4a(cb)2 [53]
24. b5acbc ⇒ a2dba2cbcb4 [57]
25. b5acba ⇒ a2dbc2b5 [55]
26. b5abac ⇒ db4a(cb)2a [56]
27. b5aba2c ⇒ db4a(cb)2a2 [58]
# ab:aabbbbbaaba=1 reversed:cda/b aaa=c,bbbbbaab=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
baabc=aabcb
bcbd=adbaab
baabac=aabcba
bcbad=adbaaba
baabaac=aabcbaa
bcbaad=adbaabaa
bcbbd=adbbaab
bcbbad=adbbaaba
bcbbaad=adbbaabaa
bcbbbd=adbbbaab
bcbbbad=adbbbaaba
bcbbbaad=adbbbaabaa
bcbbbbd=adbbbbaab
bcbbbba=abbbbbc
bbbbaaba=cbbbbb
bbbbbaa=aadbcbbbb
bcbbbbb=ad
bbbbbabc=dbbbbacbcb
bbbbbacbc=aadbaacbcbbbb
bbbbbacba=aadbccbbbbb
bbbbbabac=dbbbbacbcba
bbbbbabaac=dbbbbacbcbaa

Isomorphic instances

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

1 total

Σ#PresentationMapping
113199⟨a, b | abaaabbbbba=1⟩φ(a) = a, φ(b) = b