#2890 ⟨a, b | aaaabbbabba=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 [13]
2. dc ⇒ 1 [20]
3. ac ⇒ ca [5]
4. ad ⇒ da [19]
5. a5 ⇒ c [2]
6. cb3 ⇒ bab2a4 [25]
7. dbab2 ⇒ b3da [21]
8. ab2cb ⇒ bab2c [32]
9. cab3 ⇒ abab2a4 [26]
10. dabab2 ⇒ ab3da [24]
11. ca2b3 ⇒ a2bab2a4 [33]
12. da2bab2 ⇒ a2b3da [23]
13. ca3b3 ⇒ a3bab2a4 [37]
14. da3bab2 ⇒ a3b3da [34]
15. a4b3 ⇒ b2cbda4 [39]
16. a4bab2 ⇒ cb2cbd [31]
17. db2ab2 ⇒ b3abd [12]
18. d(ab2)2 ⇒ ab3abd [29]
19. da(ab2)2 ⇒ a2b3abd [36]
20. da2(ab2)2 ⇒ a3b3abd [40]
21. a3(ab2)2 ⇒ (cb2)2d [41]
22. b3ab2 ⇒ d [3]
# ab:aaaabbbabba=1 cda/b aaaaa=c,bbbabb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaaaa=c
cbbb=babbaaaa
dbabb=bbbda
abbcb=babbc
cabbb=ababbaaaa
dababb=abbbda
caabbb=aababbaaaa
daababb=aabbbda
caaabbb=aaababbaaaa
daaababb=aaabbbda
aaaabbb=bbcbdaaaa
aaaababb=cbbcbd
dbbabb=bbbabd
dabbabb=abbbabd
daabbabb=aabbbabd
daaabbabb=aaabbbabd
aaaabbabb=cbbcbbd
bbbabb=d

Isomorphic instances

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

1 total

Σ#PresentationMapping
112989⟨a, b | aaabbbabbaa=1⟩φ(a) = a, φ(b) = b