#2766 ⟨a, b | babab=aabaa⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. a2ba2 ⇒ b(ab)2 [1]
2. a2b2(ab)2 ⇒ (ba)2b2a2 [2]
3. a(ab)4 ⇒ (ba)4a [3]
# ab:babab=aabaa ba - -
aabaa=babab
aabbabab=bababbaa
aabababab=babababaa

Other submonoids of same group

5 unique, 8 total

Σ#PresentationPropertiesφ
8388⟨a, b | aabbbaa=b⟩Can Inf
8520⟨a, b | aabaa=bbb⟩Can Inf
101360⟨a, b | aaababbaba=1⟩Grp Inf3
101694⟨a, b | aabababaa=b⟩Can Inf
102066⟨a, b | ababbaba=bb⟩Can Inf