#4843 ⟨a, b | ababbaba=bab⟩

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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. bc ⇒ c2a [6]
2. bab ⇒ abac [3]
3. abac2 ⇒ bac2a [8]
4. aba(ca)2 ⇒ c [4]
5. b2ac ⇒ cbaca [10]
6. ba2bac ⇒ abacab [5]
7. abacac2 ⇒ cba(ca)2 [7]
8. a(bac)2 ⇒ (bac)2a [12]
9. a(baca)2 ⇒ bac [9]
10. ab(ac)2bac ⇒ c(baca)2 [11]
# ab:ababbaba=bab a/cb bbaba=c morph:5/0
bc=cca
bab=abac
abacc=bacca
abacaca=c
bbac=cbaca
baabac=abacab
abacacc=cbacaca
abacbac=bacbaca
abacabaca=bac
abacacbac=cbacabaca

Other submonoids of same group

11 unique, 23 total

Σ#PresentationPropertiesφ
7182⟨a, b | aabbaa=b⟩Can Inf1
7214⟨a, b | aabaa=bb⟩Can Inf
8378⟨a, b | aababaa=b⟩Can Inf
8519⟨a, b | aabaa=bab⟩Can Inf
9672⟨a, b | aababbaba=1⟩Grp Inf10
9796⟨a, b | aabaabaa=b⟩Can Inf
9854⟨a, b | ababbaba=b⟩Can Inf1
91204⟨a, b | aabaa=baab⟩Can Inf
101670⟨a, b | aabaaabaa=b⟩Can Inf
102743⟨a, b | baaab=aabaa⟩Can Inf
115943⟨a, b | abbbba=bbabb⟩Can Inf