#1204 ⟨a, b | aabaa=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. a2 ⇒ c [2]
2. bd ⇒ dc [5]
3. ca ⇒ ac [6]
4. cb ⇒ d [3]
5. cd2 ⇒ d2b [8]
6. cdc ⇒ d2 [7]
7. cdad ⇒ d2ab [10]
8. cdac ⇒ d2a [9]
# ab:aabaa=baab adbc aa=c,cb=d morph:2/0,2/0
aa=c
bd=dc
ca=ac
cb=d
cdd=ddb
cdc=dd
cdad=ddab
cdac=dda

Other submonoids of same group

11 unique, 23 total

Σ#PresentationDescriptionRelated
7182⟨a, b | aabbaa=b⟩Infinite cancellative non-commutative monoid1 iso
7214⟨a, b | aabaa=bb⟩Infinite cancellative non-commutative monoid
8378⟨a, b | aababaa=b⟩Infinite cancellative non-commutative monoid
8519⟨a, b | aabaa=bab⟩Infinite cancellative non-commutative monoid
9672⟨a, b | aababbaba=1⟩Infinite non-Abelian group10 iso
9796⟨a, b | aabaabaa=b⟩Infinite cancellative non-commutative monoid
9854⟨a, b | ababbaba=b⟩Infinite cancellative non-commutative monoid1 iso
101670⟨a, b | aabaaabaa=b⟩Infinite cancellative non-commutative monoid
102743⟨a, b | baaab=aabaa⟩Infinite cancellative non-commutative monoid
114843⟨a, b | ababbaba=bab⟩Infinite cancellative non-commutative monoid
115943⟨a, b | abbbba=bbabb⟩Infinite cancellative non-commutative monoid