#2325 ⟨a, b | ababaab=baa⟩

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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. cacb2 ⇒ abc [9]
2. cbacb ⇒ bac [5]
3. abacb ⇒ c [4]
4. ba2 ⇒ c [2]
5. ca2 ⇒ abac2 [6]
6. c(ba)2c ⇒ b(ac)2b [8]
7. a(ba)2c ⇒ cacb [7]
# ab:ababaab=baa bc/a baa=c magic:0
cacbb=abc
cbacb=bac
abacb=c
baa=c
caa=abacc
cbabac=bacacb
ababac=cacb

Other submonoids of same group

5 unique, 5 total

Σ#PresentationDescriptionRelated
8459⟨a, b | aabbab=ba⟩Infinite cancellative non-commutative monoid
8543⟨a, b | abaab=bba⟩Infinite cancellative non-commutative monoid
101960⟨a, b | aababaab=ba⟩Infinite cancellative non-commutative monoid
102028⟨a, b | abaaabab=ba⟩Infinite cancellative non-commutative monoid
102573⟨a, b | abaaab=baba⟩Infinite cancellative non-commutative monoid