#5694 ⟨a, b | aababa=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. a2b ⇒ c [2]
2. caba ⇒ bac [4]
3. bacab ⇒ cabc [5]
4. (ba)2c ⇒ cabca [8]
5. a2cabc ⇒ (ca)2b [6]
6. (ca)2bc ⇒ bac2ab [7]
7. a2cab2ac ⇒ bac2ba [9]
8. (ca)2b2ac ⇒ ba(cba)2 [10]
# ab:aababa=baaab reversed:abc aab=c morph:3/0
aab=c
caba=bac
bacab=cabc
babac=cabca
aacabc=cacab
cacabc=baccab
aacabbac=baccba
cacabbac=bacbacba

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
91232⟨a, b | aabba=baab⟩Infinite cancellative non-commutative monoid
115332⟨a, b | abaabba=baab⟩Infinite cancellative non-commutative monoid