#1262 ⟨a, b | ababa=baab⟩

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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 [17]
2. ad2 ⇒ d2a [19]
3. cd ⇒ da2ca3 [20]
4. cad ⇒ da2ca2 [9]
5. ca2d ⇒ da2ca [8]
6. ca3d ⇒ da2c [15]
7. ca2c ⇒ dab [6]
8. ca3ca ⇒ da2b [11]
9. ca2b ⇒ d [3]
10. bd ⇒ daba2 [18]
11. bad ⇒ daba [7]
12. ba2d ⇒ dab [14]
13. ba3d ⇒ aca3c [16]
14. bac ⇒ cab [5]
15. ba2c ⇒ ad [12]
16. ba3ca ⇒ aca3b [13]
17. bab ⇒ c [2]
18. ba2b ⇒ aca [4]
# ab:ababa=baab a/dcb bab=c,caab=d morph:3/2,4/1
ada=d
add=dda
cd=daacaaa
cad=daacaa
caad=daaca
caaad=daac
caac=dab
caaaca=daab
caab=d
bd=dabaa
bad=daba
baad=dab
baaad=acaaac
bac=cab
baac=ad
baaaca=acaaab
bab=c
baab=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
102361⟨a, b | abbbbba=bab⟩Infinite cancellative non-commutative monoid
114887⟨a, b | abbbbbba=bab⟩Infinite cancellative non-commutative monoid
115855⟨a, b | abaaba=baaab⟩Infinite cancellative non-commutative monoid