#586 ⟨a, b | baab=aaba⟩

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  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. bc ⇒ ca [4]
2. a2c ⇒ cab [5]
3. a2ba ⇒ c [2]
4. ba2b ⇒ c [3]
# ab:baab=aaba cab aaba=c magic:0
bc=ca
aac=cab
aaba=c
baab=c

Other submonoids of same group

12 unique, 56 total

Σ#PresentationDescriptionRelated
6104⟨a, b | aaba=bb⟩Infinite cancellative non-commutative monoid
7145⟨a, b | aababba=1⟩Infinite non-Abelian group22 iso, 22 anti-iso
7193⟨a, b | ababba=b⟩Infinite cancellative non-commutative monoid
7252⟨a, b | aaba=bab⟩Infinite cancellative non-commutative monoid
9842⟨a, b | abaababa=b⟩Infinite cancellative non-commutative monoid
91126⟨a, b | ababba=bab⟩Infinite cancellative non-commutative monoid
91273⟨a, b | abbba=babb⟩Infinite cancellative non-commutative monoid
102633⟨a, b | abbbba=babb⟩Infinite cancellative non-commutative monoid
113716⟨a, b | abaaabaaba=b⟩Infinite cancellative non-commutative monoid
114876⟨a, b | abbabbba=bab⟩Infinite cancellative non-commutative monoid
115415⟨a, b | abbbbba=babb⟩Infinite cancellative non-commutative monoid
115898⟨a, b | ababba=babab⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

6 unique, 6 total

Σ#PresentationDescriptionRelated
687⟨a, b | aabba=b⟩Infinite cancellative non-commutative monoid
7179⟨a, b | aababa=b⟩Infinite cancellative non-commutative monoid
8374⟨a, b | aabaaba=b⟩Infinite cancellative non-commutative monoid
9792⟨a, b | aabaaaba=b⟩Infinite cancellative non-commutative monoid
101666⟨a, b | aabaaaaba=b⟩Infinite cancellative non-commutative monoid
113536⟨a, b | aabaaaaaba=b⟩Infinite cancellative non-commutative monoid