#3111 ⟨a, b | aabbaabbaba=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 [11]
2. dc ⇒ 1 [18]
3. bc ⇒ cb [5]
4. bd ⇒ db [17]
5. b2 ⇒ c [2]
6. ba3 ⇒ acabad [24]
7. bacaba ⇒ ca3c [25]
8. ca2caba ⇒ (aca)2b [29]
9. d(aca)2 ⇒ a2cabadb [34]
10. cba2caba ⇒ b(aca)2b [28]
11. db(aca)2 ⇒ ba2cabadb [35]
12. d(a2c)2a ⇒ a2caba2db [41]
13. b(a2c)2a ⇒ ca3ca2b [39]
14. ba2caba2 ⇒ a(a2c)2 [30]
15. b(ac)2a3 ⇒ ca3c2abad [42]
16. a(a2c)2a ⇒ db [19]
17. ca(ac)2a3 ⇒ (aca)2c(ba)2d [43]
18. cba(ac)2a3 ⇒ b(aca)2c(ba)2d [44]
19. baca4ca2 ⇒ ca3(ca)2ba2d [45]
20. c(a2ca2)2 ⇒ (a2c)2acbaba2d [47]
21. b(a2ca2)2 ⇒ a3ca2c2aba2d [46]
22. ba2c(aca2)2 ⇒ a3(ca2c)2adb [49]
# ab:aabbaabbaba=1 cdb/a bb=c,aabbabaaa=d magic:1
cd=1
dc=1
bc=cb
bd=db
bb=c
baaa=acabad
bacaba=caaac
caacaba=acaacab
dacaaca=aacabadb
cbaacaba=bacaacab
dbacaaca=baacabadb
daacaaca=aacabaadb
baacaaca=caaacaab
baacabaa=aaacaac
bacacaaa=caaaccabad
aaacaaca=db
caacacaaa=acaacacbabad
cbaacacaaa=bacaacacbabad
bacaaaacaa=caaacacabaad
caacaaaacaa=aacaacacbabaad
baacaaaacaa=aaacaaccabaad
baacacaaacaa=aaacaaccaacadb

Isomorphic instances

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

3 total

Σ#PresentationMapping
113117⟨a, b | aabbabaaabb=1⟩φ(a) = a, φ(b) = b
113261⟨a, b | ababbbaabba=1⟩φ(a) = b, φ(b) = a
113280⟨a, b | abbaababbba=1⟩φ(a) = b, φ(b) = a