#2044 ⟨a, b | abaabbab=ba⟩

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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. (c2b)2bab ⇒ bac [10]
2. acb2ab ⇒ ba [3]
3. acb2ac ⇒ ca [5]
4. acbc2b2ab ⇒ c [9]
5. ba2 ⇒ c [2]
6. (ba)2 ⇒ c2b2ab [4]
7. baca ⇒ c2b2ac [6]
8. ca2 ⇒ acbc2b2ac [17]
9. cab2ab ⇒ acb3a [7]
10. cab2ac ⇒ acb2ca [8]
11. cabc2b2ab ⇒ acb2c [15]
12. c2(b2a)2 ⇒ bac2b2ab [12]
13. c2b2abca ⇒ bac2b2ac [16]
14. c(cb2ab)2 ⇒ bab2a [11]
15. c2b2abcb2ac ⇒ babca [13]
16. (c2b2a)2b ⇒ bacba [18]
17. (c2b2a)2c ⇒ bac2a [19]
18. c2b2abcbc2b2ab ⇒ babc [14]
# ab:abaabbab=ba bc/a baa=c morph:3/0
ccbccbbab=bac
acbbab=ba
acbbac=ca
acbccbbab=c
baa=c
baba=ccbbab
baca=ccbbac
caa=acbccbbac
cabbab=acbbba
cabbac=acbbca
cabccbbab=acbbc
ccbbabba=baccbbab
ccbbabca=baccbbac
ccbbabcbbab=babba
ccbbabcbbac=babca
ccbbaccbbab=bacba
ccbbaccbbac=bacca
ccbbabcbccbbab=babc

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
91109⟨a, b | abaaab=bba⟩Infinite cancellative non-commutative monoid
101994⟨a, b | aabbabab=ba⟩Infinite cancellative non-commutative monoid
115291⟨a, b | abaaaab=baba⟩Infinite cancellative non-commutative monoid