#3434 ⟨a, b | aaabaaabaa=b⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic 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. a3b2 ⇒ baba2 [2]
2. (a3b)2ab ⇒ ba(aba2)2 [3]
3. (a3b)2a2 ⇒ b [1]
# ab:aaabaaabaa=b ba - -
aaabb=babaa
aaabaaabab=baabaaabaa
aaabaaabaa=b

Other submonoids of same group

6 unique, 11 total

Σ#PresentationPropertiesφ
8431⟨a, b | aaabaa=bb⟩Can Inf
91038⟨a, b | aaabaa=bab⟩Can Inf
102430⟨a, b | aaabaa=baab⟩Can Inf
113070⟨a, b | aabababbaba=1⟩Grp Inf5
113775⟨a, b | abababbaba=b⟩Can Inf
115550⟨a, b | aaabaa=baaab⟩Can Inf

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationProperties
8366⟨a, b | aaabbaa=b⟩Can Inf
9769⟨a, b | aaababaa=b⟩Can Inf
101616⟨a, b | aaabaabaa=b⟩Can Inf