#5550 ⟨a, b | aaabaa=baaab⟩

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Quick links

  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. a2 ⇒ c [2]
2. ab ⇒ d [3]
3. ac ⇒ ca [6]
4. ad ⇒ cb [7]
5. bcd ⇒ cdc [5]
6. c2bc ⇒ dcd [8]
7. c3dc ⇒ dcd2 [9]
8. c2bdcd ⇒ (dc)2bc [10]
9. c3d2cd ⇒ dcd2cbc [11]
# ab:aaabaa=baaab reversed:abcd aa=c,ab=d morph:2/0,2/0
aa=c
ab=d
ac=ca
ad=cb
bcd=cdc
ccbc=dcd
cccdc=dcdd
ccbdcd=dcdcbc
cccddcd=dcddcbc

Other submonoids of same group

5 unique, 10 total

Σ#PresentationDescriptionRelated
8431⟨a, b | aaabaa=bb⟩Infinite cancellative non-commutative monoid
91038⟨a, b | aaabaa=bab⟩Infinite cancellative non-commutative monoid
102430⟨a, b | aaabaa=baab⟩Infinite cancellative non-commutative monoid
113070⟨a, b | aabababbaba=1⟩Infinite non-Abelian group1 iso, 4 anti-iso
113775⟨a, b | abababbaba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

4 unique, 4 total

Σ#PresentationDescriptionRelated
8366⟨a, b | aaabbaa=b⟩Infinite cancellative non-commutative monoid
9769⟨a, b | aaababaa=b⟩Infinite cancellative non-commutative monoid
101616⟨a, b | aaabaabaa=b⟩Infinite cancellative non-commutative monoid
113434⟨a, b | aaabaaabaa=b⟩Infinite cancellative non-commutative monoid