#1502 ⟨a, b | abaabbbaab=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. ac ⇒ ca [5]
2. a2 ⇒ c [2]
3. dc ⇒ 1 [23]
4. cd ⇒ 1 [11]
5. ad ⇒ da [24]
6. cbabcb ⇒ bcbabc [38]
7. ab2cb ⇒ cbcb2da [30]
8. abcb2 ⇒ b2cba [26]
9. c(ab)2cb ⇒ abcbabc [39]
10. dbcbab ⇒ babcbd [36]
11. dabcbab ⇒ (ab)2cbd [37]
12. cb3cb ⇒ b2c(ba)2 [17]
13. ab3cb ⇒ bcb3a [32]
14. db2cbab ⇒ b3cbda [31]
15. b3cbab ⇒ d [3]
16. (cb)3b2 ⇒ bcb(abc)2bd [46]
17. ca(bc)2b3 ⇒ abcb(abc)2bd [47]
18. d(bc)3b2 ⇒ babcbdbcba [48]
19. da(bc)3b2 ⇒ (ab)2cbdbcba [49]
20. db(bc)3b2 ⇒ b3cbdabcba [53]
21. db(bc)2ab3 ⇒ (ab)2cbdb2cbda [52]
22. dbcb2cb3 ⇒ babcbdb2cbda [51]
23. b3(cb)3b ⇒ dbcba [28]
24. d(b2c)2b3 ⇒ b3(cb2)2d [45]
25. b(b2c)2b3 ⇒ db2cbda [44]
# ab:abaabbbaab=1 ca/d/b aa=c,bbbaabab=d magic:0
ac=ca
aa=c
dc=1
cd=1
ad=da
cbabcb=bcbabc
abbcb=cbcbbda
abcbb=bbcba
cababcb=abcbabc
dbcbab=babcbd
dabcbab=ababcbd
cbbbcb=bbcbaba
abbbcb=bcbbba
dbbcbab=bbbcbda
bbbcbab=d
cbcbcbbb=bcbabcabcbd
cabcbcbbb=abcbabcabcbd
dbcbcbcbb=babcbdbcba
dabcbcbcbb=ababcbdbcba
dbbcbcbcbb=bbbcbdabcba
dbbcbcabbb=ababcbdbbcbda
dbcbbcbbb=babcbdbbcbda
bbbcbcbcbb=dbcba
dbbcbbcbbb=bbbcbbcbbd
bbbcbbcbbb=dbbcbda

Isomorphic instances

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

1 total

Σ#PresentationMapping
101510⟨a, b | ababaabbba=1⟩φ(a) = a, φ(b) = b