#2966 ⟨a, b | aaabbaabbba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-isomorphic instances

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. dc ⇒ 1 [18]
2. cd ⇒ 1 [34]
3. cb ⇒ bc [5]
4. db ⇒ bd [35]
5. b3 ⇒ c [2]
6. ab2a2c ⇒ b2a2ca [54]
7. a2cad ⇒ bdab2a2 [55]
8. ab2a2bc ⇒ b2a2cab [47]
9. a2cabd ⇒ bdab2a2b [48]
10. ab2a2b2c ⇒ b2a2cab2 [50]
11. a2cab2d ⇒ bdab2a2b2 [51]
12. a2ca2d ⇒ bda2b2a2 [57]
13. a2ca2b ⇒ ba4c [43]
14. a2b2a2b ⇒ ca4 [46]
15. a4b2 ⇒ b2da2ca2 [38]
16. a2ca3d ⇒ bda3b2a2 [59]
17. a2ca3b ⇒ bdaca4c [61]
18. a2ca4 ⇒ bd [36]
19. a4ba2c ⇒ da2b(ca2)2 [62]
20. a4bca2c ⇒ b2da2b2(ca2)2 [66]
21. a4ba2b ⇒ da2b2ca4 [65]
22. a4bca2b ⇒ b2da2c2a4 [64]
# ab:aaabbaabbba=1 reversed:cdb/a bbb=c,aaaabbaa=d magic:1
dc=1
cd=1
cb=bc
db=bd
bbb=c
abbaac=bbaaca
aacad=bdabbaa
abbaabc=bbaacab
aacabd=bdabbaab
abbaabbc=bbaacabb
aacabbd=bdabbaabb
aacaad=bdaabbaa
aacaab=baaaac
aabbaab=caaaa
aaaabb=bbdaacaa
aacaaad=bdaaabbaa
aacaaab=bdacaaaac
aacaaaa=bd
aaaabaac=daabcaacaa
aaaabcaac=bbdaabbcaacaa
aaaabaab=daabbcaaaa
aaaabcaab=bbdaaccaaaa

Isomorphic instances

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

4 total

Σ#PresentationMapping
113112⟨a, b | aabbaabbbaa=1⟩φ(a) = a, φ(b) = b
113136⟨a, b | aabbbaaaabb=1⟩φ(a) = a, φ(b) = b
113155⟨a, b | aabbbbaabba=1⟩φ(a) = b, φ(b) = a
113276⟨a, b | abbaaabbbba=1⟩φ(a) = b, φ(b) = a

Anti-isomorphic instances

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

3 total

Σ#PresentationMapping
112985⟨a, b | aaabbbaabba=1⟩φ(a) = a, φ(b) = b
113114⟨a, b | aabbaabbbba=1⟩φ(a) = b, φ(b) = a
113272⟨a, b | abbaaaabbba=1⟩φ(a) = a, φ(b) = b