#5855 ⟨a, b | abaaba=baaab⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. ada ⇒ d [15]
2. ad2 ⇒ d2a [16]
3. cd ⇒ da3ca4 [22]
4. cad ⇒ da3ca3 [20]
5. ca2d ⇒ da3ca2 [18]
6. ca3d ⇒ da3ca [17]
7. ca4d ⇒ da3c [13]
8. ca3c ⇒ da2b [6]
9. ca4ca ⇒ da3b [9]
10. ca3b ⇒ d [3]
11. bd ⇒ da2ba3 [21]
12. bad ⇒ da2ba2 [19]
13. ba2d ⇒ da2ba [7]
14. ba3d ⇒ da2b [12]
15. ba4d ⇒ aca4c [14]
16. ba2c ⇒ ca2b [5]
17. ba3c ⇒ ad [10]
18. ba4ca ⇒ aca4b [11]
19. ba2b ⇒ c [2]
20. ba3b ⇒ aca [4]
# ab:abaaba=baaab a/dcb baab=c,caaab=d morph:4/0,5/0
ada=d
add=dda
cd=daaacaaaa
cad=daaacaaa
caad=daaacaa
caaad=daaaca
caaaad=daaac
caaac=daab
caaaaca=daaab
caaab=d
bd=daabaaa
bad=daabaa
baad=daaba
baaad=daab
baaaad=acaaaac
baac=caab
baaac=ad
baaaaca=acaaaab
baab=c
baaab=aca

Other submonoids of same group

12 unique, 57 total

Σ#PresentationDescriptionRelated
530⟨a, b | aabba=1⟩Infinite non-Abelian group40 iso
543⟨a, b | abba=b⟩Infinite cancellative non-commutative monoid
546⟨a, b | aaa=bb⟩Infinite cancellative non-commutative monoid
553⟨a, b | aba=bb⟩Infinite cancellative non-commutative monoid
691⟨a, b | ababa=b⟩Infinite cancellative non-commutative monoid5 iso
6123⟨a, b | bab=aba⟩Infinite cancellative non-commutative monoid
7267⟨a, b | abba=bab⟩Infinite cancellative non-commutative monoid
8555⟨a, b | abbba=bab⟩Infinite cancellative non-commutative monoid
91137⟨a, b | abbbba=bab⟩Infinite cancellative non-commutative monoid
91262⟨a, b | ababa=baab⟩Infinite cancellative non-commutative monoid
102361⟨a, b | abbbbba=bab⟩Infinite cancellative non-commutative monoid
114887⟨a, b | abbbbbba=bab⟩Infinite cancellative non-commutative monoid