#3490 ⟨a, b, c | bb=aa, acb=c⟩

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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. a2d ⇒ da2 [12]
2. ba3 ⇒ ad [9]
3. aba ⇒ d [3]
4. a2b ⇒ ba2 [5]
5. d2 ⇒ a6 [19]
6. dab ⇒ a5 [8]
7. bda ⇒ adb [14]
8. bad ⇒ a5 [10]
9. abd ⇒ dba [4]
10. b2 ⇒ a2 [1]
11. bdba2 ⇒ adbab [16]
12. aca2 ⇒ cb [6]
13. acda ⇒ cbab [18]
14. acad ⇒ ca3 [11]
15. acb ⇒ c [2]
16. acdba2 ⇒ cbdb [21]
17. bc ⇒ adcba2 [23]
18. bac ⇒ adca2 [22]
19. ba2c ⇒ adcb [13]
20. bdc ⇒ (ad)2ca4 [24]
21. ac2 ⇒ (cad)2a [26]
22. (ac)2 ⇒ cadca4 [25]
23. acdc ⇒ c(ad)2ca6 [27]
# abc:bb=aa,acb=c a/db/c aba=d morph:3/0
aad=daa
baaa=ad
aba=d
aab=baa
dd=aaaaaa
dab=aaaaa
bda=adb
bad=aaaaa
abd=dba
bb=aa
bdbaa=adbab
acaa=cb
acda=cbab
acad=caaa
acb=c
acdbaa=cbdb
bc=adcbaa
bac=adcaa
baac=adcb
bdc=adadcaaaa
acc=cadcada
acac=cadcaaaa
acdc=cadadcaaaaaa

Other submonoids of same group

2 unique, 21 total

Σ#PresentationPropertiesφ
7930⟨a, b, c | aa=b, bcb=c⟩Can Inf4
82179⟨a, b, c | aabb=1, bacc=1⟩Grp Inf15