#2883 ⟨a, b | aaaabbabbba=1⟩

Up:Monoid enumeration
Prev:#2882 ⟨a, b | aaaabbabbab=1⟩
Next:#2885 ⟨a, b | aaaabbbaaab=1⟩

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 [14]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [13]
5. a5 ⇒ c [2]
6. b3c ⇒ a4b2ab [18]
7. b2abd ⇒ adb3 [15]
8. bcb2a ⇒ cb2ab [25]
9. b3ac ⇒ a4b(ba)2 [20]
10. b(ba)2d ⇒ adb3a [16]
11. b3a2c ⇒ a4b2aba2 [27]
12. b2aba2d ⇒ adb3a2 [21]
13. b3a3c ⇒ a4b2aba3 [31]
14. b2aba3d ⇒ adb3a3 [28]
15. b3a4 ⇒ a4dbcb2 [33]
16. b2aba4 ⇒ dbcb2c [26]
17. b2ab2d ⇒ dbab3 [10]
18. (b2a)2d ⇒ dbab3a [22]
19. (b2a)2ad ⇒ dbab3a2 [30]
20. b2ab2a3d ⇒ dbab3a3 [34]
21. b2ab2a4 ⇒ d(b2c)2 [35]
22. b2ab3 ⇒ d [3]
# ab:aaaabbabbba=1 reversed:cda/b aaaaa=c,bbabbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaa=c
bbbc=aaaabbab
bbabd=adbbb
bcbba=cbbab
bbbac=aaaabbaba
bbabad=adbbba
bbbaac=aaaabbabaa
bbabaad=adbbbaa
bbbaaac=aaaabbabaaa
bbabaaad=adbbbaaa
bbbaaaa=aaaadbcbb
bbabaaaa=dbcbbc
bbabbd=dbabbb
bbabbad=dbabbba
bbabbaad=dbabbbaa
bbabbaaad=dbabbbaaa
bbabbaaaa=dbbcbbc
bbabbb=d

Isomorphic instances

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

3 total

Σ#PresentationMapping
112977⟨a, b | aaabbabbbaa=1⟩φ(a) = a, φ(b) = b
113161⟨a, b | aabbbbbaaba=1⟩φ(a) = b, φ(b) = a
113199⟨a, b | abaaabbbbba=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.

4 total

Σ#PresentationMapping
112890⟨a, b | aaaabbbabba=1⟩φ(a) = a, φ(b) = b
112989⟨a, b | aaabbbabbaa=1⟩φ(a) = a, φ(b) = b
113051⟨a, b | aabaabbbbba=1⟩φ(a) = b, φ(b) = a
113160⟨a, b | aabbbbbaaab=1⟩φ(a) = b, φ(b) = a