#3716 ⟨a, b | abaaabaaba=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. aba3bab ⇒ b(a2b)2a [2]
2. (aba2)2ba ⇒ b [1]
3. (aba2)2b2 ⇒ b2a(a2b)2a [3]
4. (aba3)2b2 ⇒ baba3(aba)2 [7]
5. (ba2)3a(ab)2 ⇒ aba3b2(a2b)2a [5]
6. a(ba3)3b2 ⇒ bab(a2ba2)2ba [8]
7. (ba2)3(a2b)2a ⇒ aba3b2 [4]
8. (ba2)3(a2b)2b ⇒ aba3b3a(a2b)2a [6]
9. (ba2)3(a3b)2b ⇒ aba3b2aba3(aba)2 [9]
10. b(a2b)2a(a3b)3b ⇒ aba3b2ab(a2ba2)2ba [10]
# ab:abaaabaaba=b reversed:ab - -
abaaabab=baabaaba
abaaabaaba=b
abaaabaabb=bbaaabaaba
abaaaabaaabb=babaaaabaaba
baabaabaaaabab=abaaabbaabaaba
abaaabaaabaaabb=babaabaaaabaaba
baabaabaaaabaaba=abaaabb
baabaabaaaabaabb=abaaabbbaaabaaba
baabaabaaaaabaaabb=abaaabbabaaaabaaba
baabaabaaaabaaabaaabb=abaaabbabaabaaaabaaba

Other submonoids of same group

11 unique, 55 total

Σ#PresentationPropertiesφ
6104⟨a, b | aaba=bb⟩Can Inf
7145⟨a, b | aababba=1⟩Grp Inf44
7193⟨a, b | ababba=b⟩Can Inf
7252⟨a, b | aaba=bab⟩Can Inf
9842⟨a, b | abaababa=b⟩Can Inf
91126⟨a, b | ababba=bab⟩Can Inf
91273⟨a, b | abbba=babb⟩Can Inf
102633⟨a, b | abbbba=babb⟩Can Inf
114876⟨a, b | abbabbba=bab⟩Can Inf
115415⟨a, b | abbbbba=babb⟩Can Inf
115898⟨a, b | ababba=babab⟩Can Inf

Other submonoids of anti-isomorphic group

7 unique, 7 total

Σ#PresentationProperties
687⟨a, b | aabba=b⟩Can Inf
7179⟨a, b | aababa=b⟩Can Inf
8374⟨a, b | aabaaba=b⟩Can Inf
8586⟨a, b | baab=aaba⟩Can Inf
9792⟨a, b | aabaaaba=b⟩Can Inf
101666⟨a, b | aabaaaaba=b⟩Can Inf
113536⟨a, b | aabaaaaaba=b⟩Can Inf