#3051 ⟨a, b | aabaabbbbba=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. cba2b ⇒ bcba2 [26]
7. dbcb ⇒ ba2bda [17]
8. caba2b ⇒ abcba2 [27]
9. dabcb ⇒ aba2bda [21]
10. c(a2b)2 ⇒ a2bcba2 [29]
11. da2bcb ⇒ (a2b)2da [30]
12. db2cb ⇒ ba2b2da [18]
13. dab2cb ⇒ aba2b2da [22]
14. da2b2cb ⇒ (a2b)2bda [32]
15. db3cb ⇒ ba2b3da [19]
16. dab3cb ⇒ aba2b3da [23]
17. da2b3cb ⇒ a2ba2b3da [34]
18. db4cb ⇒ ba2b4da [20]
19. ab4cb ⇒ cb5a [33]
20. aba2b4 ⇒ b5c [15]
21. a2b5 ⇒ b4cbda2 [31]
22. b5cb ⇒ da [16]
23. cbab5 ⇒ (bc)2ab4d [35]
24. cbcab5 ⇒ b4cbca2bda2 [39]
25. abcab5 ⇒ b5c2bda2 [37]
26. cabab5 ⇒ a(bc)2ab4d [38]
27. ca2bab5 ⇒ a2(bc)2ab4d [40]
# ab:aabaabbbbba=1 cda/b aaa=c,baabbbbb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
cbaab=bcbaa
dbcb=baabda
cabaab=abcbaa
dabcb=abaabda
caabaab=aabcbaa
daabcb=aabaabda
dbbcb=baabbda
dabbcb=abaabbda
daabbcb=aabaabbda
dbbbcb=baabbbda
dabbbcb=abaabbbda
daabbbcb=aabaabbbda
dbbbbcb=baabbbbda
abbbbcb=cbbbbba
abaabbbb=bbbbbc
aabbbbb=bbbbcbdaa
bbbbbcb=da
cbabbbbb=bcbcabbbbd
cbcabbbbb=bbbbcbcaabdaa
abcabbbbb=bbbbbccbdaa
cababbbbb=abcbcabbbbd
caababbbbb=aabcbcabbbbd

Isomorphic instances

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

1 total

Σ#PresentationMapping
113160⟨a, b | aabbbbbaaab=1⟩φ(a) = a, φ(b) = b