#467 ⟨a, b | abaaab=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 [5]
2. a3b ⇒ c [2]
3. ba ⇒ c4ab [7]
4. bc ⇒ c8b [8]
# ab:abaaab=ba reversed:ac/b aaab=c morph:4/0
acc=ca
aaab=c
ba=ccccab
bc=ccccccccb

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
7225⟨a, b | abaab=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