#1467 ⟨a, b | aabbbbaaba=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 [9]
2. dc ⇒ 1 [11]
3. ac ⇒ ca [5]
4. ad ⇒ da [10]
5. a3 ⇒ c [2]
6. aba2b ⇒ (cb)2d [23]
7. a2bcb ⇒ ba2bc [19]
8. ab2a2b ⇒ cbcb2d [26]
9. (abc)2b ⇒ (cb)2da2bc [38]
10. cb4 ⇒ b3a2ba [14]
11. db3a2b ⇒ b4da2 [12]
12. ab4 ⇒ bcb3da [33]
13. ab3a2b ⇒ cbcb3d [30]
14. ab2cabcb ⇒ cbcb2da2bc [39]
15. b4a2b ⇒ d [3]
16. db3cabcb ⇒ b4abc [22]
17. ab3cabcb ⇒ cbcb3da2bc [41]
18. (ab)2cb3 ⇒ (cb)2db3a2 [40]
19. b4cabcb ⇒ da2bc [21]
20. ab2abcb3 ⇒ cbcb2db3a2 [42]
21. db3abcb3 ⇒ b4da2b3a2 [43]
22. ab3abcb3 ⇒ cbcb3db3a2 [44]
23. b4abcb3 ⇒ db3a2 [29]
# ab:aabbbbaaba=1 cda/b aaa=c,bbbbaab=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
abaab=cbcbd
aabcb=baabc
abbaab=cbcbbd
abcabcb=cbcbdaabc
cbbbb=bbbaaba
dbbbaab=bbbbdaa
abbbb=bcbbbda
abbbaab=cbcbbbd
abbcabcb=cbcbbdaabc
bbbbaab=d
dbbbcabcb=bbbbabc
abbbcabcb=cbcbbbdaabc
ababcbbb=cbcbdbbbaa
bbbbcabcb=daabc
abbabcbbb=cbcbbdbbbaa
dbbbabcbbb=bbbbdaabbbaa
abbbabcbbb=cbcbbbdbbbaa
bbbbabcbbb=dbbbaa

Isomorphic instances

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

1 total

Σ#PresentationMapping
101490⟨a, b | abaaabbbba=1⟩φ(a) = a, φ(b) = b