#5874 ⟨a, b | ababab=baaba⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

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. ce2 ⇒ dc [15]
2. ec2 ⇒ d [7]
3. ecdc ⇒ de2 [16]
4. dc3 ⇒ ced [17]
5. dc2dc ⇒ cede2 [22]
6. de4 ⇒ ecd2c [24]
7. e2a ⇒ c2ae [21]
8. dca ⇒ e3 [19]
9. c3a ⇒ e2 [14]
10. ceda ⇒ de2 [25]
11. e2ca ⇒ c2ac3 [29]
12. dc2a ⇒ edc [20]
13. dcea ⇒ cdae [26]
14. deda ⇒ ecde2 [23]
15. dceca ⇒ cdac3 [34]
16. de3da ⇒ ecd2e2 [27]
17. ca2 ⇒ ae [8]
18. (ca)2 ⇒ ac3 [12]
19. da2 ⇒ ecae [10]
20. daca ⇒ ecac3 [28]
21. ba2 ⇒ e [4]
22. baca ⇒ c3 [11]
23. eb ⇒ bac [9]
24. dcb ⇒ c5 [18]
25. c3b ⇒ bac2 [13]
26. cedb ⇒ dbac2 [31]
27. dc2b ⇒ ecbac2 [30]
28. dedb ⇒ ecdbac2 [32]
29. de2cb ⇒ (ec)2bac2 [35]
30. de3db ⇒ ecd2bac2 [33]
31. ab ⇒ c [2]
# ab:ababab=baaba ced/a/b ab=c,baacc=d,baa=e morph:2/0,5/1,3/0
cee=dc
ecc=d
ecdc=dee
dccc=ced
dccdc=cedee
deeee=ecddc
eea=ccae
dca=eee
ccca=ee
ceda=dee
eeca=ccaccc
dcca=edc
dcea=cdae
deda=ecdee
dceca=cdaccc
deeeda=ecddee
caa=ae
caca=accc
daa=ecae
daca=ecaccc
baa=e
baca=ccc
eb=bac
dcb=ccccc
cccb=bacc
cedb=dbacc
dccb=ecbacc
dedb=ecdbacc
deecb=ececbacc
deeedb=ecddbacc
ab=c

Other submonoids of same group

8 unique, 8 total

Σ#PresentationProperties
7210⟨a, b | aaabb=ba⟩Can Inf
8434⟨a, b | aaabab=ba⟩Can Inf
8583⟨a, b | baaa=abab⟩Can Inf
9903⟨a, b | aaabaab=ba⟩Can Inf
91120⟨a, b | ababab=baa⟩Can Inf
101883⟨a, b | aaabaaab=ba⟩Can Inf
113957⟨a, b | aaabaaaab=ba⟩Can Inf
114787⟨a, b | abaabaab=baa⟩Can Inf

Other submonoids of anti-isomorphic group

7 unique, 7 total

Σ#PresentationProperties
7245⟨a, b | aaab=bba⟩Can Inf
9942⟨a, b | aababab=ba⟩Can Inf
91247⟨a, b | abaab=baaa⟩Can Inf
102571⟨a, b | abaaab=baaa⟩Can Inf
114086⟨a, b | aabaabaab=ba⟩Can Inf
114265⟨a, b | abaababab=ba⟩Can Inf
115289⟨a, b | abaaaab=baaa⟩Can Inf