#225 ⟨a, b | abaab=ba⟩

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  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. ac2 ⇒ ca [6]
2. (ac)2b ⇒ c [4]
3. ba ⇒ acb [3]
4. bc ⇒ c4b [9]
# ab:abaab=ba reversed:ac/b baa=c morph:3/0
acc=ca
acacb=c
ba=acb
bc=ccccb

Other submonoids of same group

9 unique, 9 total

Σ#PresentationDescriptionRelated
549⟨a, b | aab=ba⟩Infinite cancellative non-commutative monoid
6110⟨a, b | abab=ba⟩Infinite cancellative non-commutative monoid
8467⟨a, b | abaaab=ba⟩Infinite cancellative non-commutative monoid
9969⟨a, b | abaaaab=ba⟩Infinite cancellative non-commutative monoid
9984⟨a, b | ababaab=ba⟩Infinite cancellative non-commutative monoid
102021⟨a, b | abaaaaab=ba⟩Infinite cancellative non-commutative monoid
114227⟨a, b | abaaaaaab=ba⟩Infinite cancellative non-commutative monoid
114258⟨a, b | abaabaaab=ba⟩Infinite cancellative non-commutative monoid
114297⟨a, b | abababaab=ba⟩Infinite cancellative non-commutative monoid