#3048 ⟨a, b | aabaabbbaba=1⟩

Up:Monoid enumeration
Prev:#3046 ⟨a, b | aabaabbabba=1⟩
Next:#3050 ⟨a, b | aabaabbbbab=1⟩

Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group
  5. Isomorphic instances
  6. 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. cb ⇒ bc [5]
2. b3 ⇒ c [2]
3. cd ⇒ 1 [24]
4. dc ⇒ 1 [16]
5. db ⇒ bd [25]
6. aba2c ⇒ caba2 [17]
7. aba2bc ⇒ caba2b [27]
8. aba2b2c ⇒ caba2b2 [31]
9. aba2d ⇒ daba2 [6]
10. aba2bd ⇒ daba2b [26]
11. aba2b2d ⇒ daba2b2 [32]
12. aba3b ⇒ bda2caba [33]
13. a2cabab2 ⇒ b2aba3c [35]
14. a3ba2b2 ⇒ b2dacaba3 [30]
15. a2caba2b2 ⇒ b2dacaba3c [36]
16. a2c2aba2b2 ⇒ b2dacaba3c2 [38]
17. acaba3c3 ⇒ ba2c3aba2b2 [41]
18. acaba3d ⇒ ba2daba2b2 [39]
19. a2caba3 ⇒ b2d [28]
# ab:aabaabbbaba=1 reversed:cb/d/a bbb=c,abaaabaa=d magic:1
cb=bc
bbb=c
cd=1
dc=1
db=bd
abaac=cabaa
abaabc=cabaab
abaabbc=cabaabb
abaad=dabaa
abaabd=dabaab
abaabbd=dabaabb
abaaab=bdaacaba
aacababb=bbabaaac
aaabaabb=bbdacabaaa
aacabaabb=bbdacabaaac
aaccabaabb=bbdacabaaacc
acabaaaccc=baacccabaabb
acabaaad=baadabaabb
aacabaaa=bbd

Other submonoids of same group

1 unique, 1 total

Σ#PresentationProperties
115144⟨a, b | aabaaba=babb⟩Can Inf

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationProperties
113655⟨a, b | aabbabbaba=b⟩Can Inf
114115⟨a, b | aababaaba=bb⟩Can Inf

Isomorphic instances

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

2 total

Σ#PresentationMapping
113089⟨a, b | aababbbabba=1⟩φ(a) = baacabaaab, φ(b) = a
113143⟨a, b | aabbbabaaab=1⟩φ(a) = a, φ(b) = baacabaaab

Anti-isomorphic instances

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

4 total

Σ#PresentationMapping
113085⟨a, b | aababbbaaba=1⟩φ(a) = a, φ(b) = abbaacabaa
113130⟨a, b | aabbabbbaba=1⟩φ(a) = abbaacabaa, φ(b) = a
113192⟨a, b | abaaababbba=1⟩φ(a) = a, φ(b) = abbaacabaa
113297⟨a, b | abbbaabaaab=1⟩φ(a) = a, φ(b) = abbaacabaa