#4334 ⟨a, b | abbaabaab=ba⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same 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. dc2bd ⇒ cb [9]
2. dc3b ⇒ cd [10]
3. (dc2)2b ⇒ c [5]
4. d2c2dcbd2 ⇒ cdb [19]
5. dc(cd)2c2bc ⇒ c3dc2b [16]
6. cbc3b ⇒ dc2bcd [14]
7. cbc2dc2b ⇒ dc2bc [11]
8. cdbc3b ⇒ d2c2dcbdcd [24]
9. cdbc2dc2b ⇒ d2c2dcbdc [21]
10. c3b2 ⇒ dc2dcbd2 [15]
11. dc2b2 ⇒ bd [7]
12. dc(cb)2 ⇒ cbc2bd [13]
13. dc2bcdb ⇒ cbdc2dcbd2 [20]
14. dc2bc4b ⇒ cbc(cd)2c2bcd [18]
15. dc2bc3dc2b ⇒ cbc(cd)2c2bc [17]
16. c3d(c2b)2 ⇒ dc(cd)3c2bcd [29]
17. c2(cdc2b)2 ⇒ dc(cd)3c2bc [27]
18. d2c2dcbcdb ⇒ cdbc2dcbd2 [25]
19. d2c2(dcb)2 ⇒ cdbc2bd [23]
20. d2c2dcbdcdb ⇒ cdbdc2dcbd2 [26]
21. d2c2dcbdc4b ⇒ cdbc(cd)2c2bcd [31]
22. d2c2dcbdc3dc2b ⇒ cdbc(cd)2c2bc [30]
23. cbc2b2 ⇒ bd2 [12]
24. cdbc2b2 ⇒ d2c2dc(bd)2 [22]
25. c4bc2bdb ⇒ dc2(dc)2bd2 [28]
26. ab ⇒ d [3]
27. ca ⇒ dc3 [8]
28. da ⇒ adc2b [6]
29. ba ⇒ dc2b [4]
# ab:abbaabaab=ba cd/b/a baa=c,ab=d morph:3/1,2/5
dccbd=cb
dcccb=cd
dccdccb=c
ddccdcbdd=cdb
dccdcdccbc=cccdccb
cbcccb=dccbcd
cbccdccb=dccbc
cdbcccb=ddccdcbdcd
cdbccdccb=ddccdcbdc
cccbb=dccdcbdd
dccbb=bd
dccbcb=cbccbd
dccbcdb=cbdccdcbdd
dccbccccb=cbccdcdccbcd
dccbcccdccb=cbccdcdccbc
cccdccbccb=dccdcdcdccbcd
cccdccbcdccb=dccdcdcdccbc
ddccdcbcdb=cdbccdcbdd
ddccdcbdcb=cdbccbd
ddccdcbdcdb=cdbdccdcbdd
ddccdcbdccccb=cdbccdcdccbcd
ddccdcbdcccdccb=cdbccdcdccbc
cbccbb=bdd
cdbccbb=ddccdcbdbd
ccccbccbdb=dccdcdcbdd
ab=d
ca=dccc
da=adccb
ba=dccb

Other submonoids of same group

2 unique, 2 total

Σ#PresentationProperties
9995⟨a, b | abbaaab=ba⟩Can Inf
114285⟨a, b | ababaaaab=ba⟩Can Inf