#5922 ⟨a, b | abbaab=baaba⟩

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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. abc ⇒ ca [5]
2. ba2c ⇒ cba2 [3]
3. ab2ac ⇒ cb2a2b [6]
4. ab2a2b ⇒ ba2ba [1]
5. ba2bac ⇒ cb2a2ba [7]
6. (ba2)2 ⇒ c [2]
7. ba2(ba)2c ⇒ c(b2a2b)2 [8]
8. a(bab)2ac ⇒ cba2b3a2b [11]
9. ba(ab)2a2b ⇒ ab2(aba)2 [4]
10. ba3b(ba)2c ⇒ cbaba2b3a2b [12]
11. abab2(aba)2 ⇒ cba2b [9]
12. ba3b2(aba)2 ⇒ cbaba2b [10]
# ab:abbaab=baaba reversed:bc/a baabaa=c morph:6/0
abc=ca
baac=cbaa
abbac=cbbaab
abbaab=baaba
baabac=cbbaaba
baabaa=c
baababac=cbbaabbbaab
ababbabac=cbaabbbaab
baababaab=abbabaaba
baaabbabac=cbabaabbbaab
ababbabaaba=cbaab
baaabbabaaba=cbabaab

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
9950⟨a, b | aabbaab=ba⟩Infinite cancellative non-commutative monoid
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

2 unique, 2 total

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