#950 ⟨a, b | aabbaab=ba⟩

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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. (a2c2a)2c2 ⇒ ca [11]
2. ba ⇒ a2c2ab [7]
3. bc ⇒ c2ab [6]
4. (a2c2a)2b2 ⇒ c [10]
# ab:aabbaab=ba reversed:ac/b baab=c morph:4/0
aaccaaaccacc=ca
ba=aaccab
bc=ccab
aaccaaaccabb=c

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
114110⟨a, b | aababaaab=ba⟩Infinite cancellative non-commutative monoid
114273⟨a, b | abaabbaab=ba⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
91132⟨a, b | abbaab=baa⟩Infinite cancellative non-commutative monoid
114815⟨a, b | ababaaab=baa⟩Infinite cancellative non-commutative monoid
115922⟨a, b | abbaab=baaba⟩Infinite cancellative non-commutative monoid