#4828 ⟨a, b | abababba=bab⟩

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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. bab ⇒ abc [3]
2. a2bcba ⇒ c [4]
3. a2(bc)2 ⇒ cabcba [7]
4. ba2bc ⇒ abcab [5]
5. a(abc)2 ⇒ cb [6]
6. abca2bc2 ⇒ bcb [9]
7. b2cb ⇒ abc2a2bc2 [11]
8. abcab2a ⇒ bc [8]
9. abc2ab2a ⇒ b2c [10]
10. b3c ⇒ abc3ab2a [12]
11. a2bcb2c ⇒ cbcab2a [13]
12. abcab2c ⇒ bcabcba [14]
13. b2cabc ⇒ (abc2a)2b [15]
# ab:abababba=bab reversed:ac/b ababba=c morph:6/1
bab=abc
aabcba=c
aabcbc=cabcba
baabc=abcab
aabcabc=cb
abcaabcc=bcb
bbcb=abccaabcc
abcabba=bc
abccabba=bbc
bbbc=abcccabba
aabcbbc=cbcabba
abcabbc=bcabcba
bbcabc=abccaabccab

Other submonoids of same group

6 unique, 24 total

Σ#PresentationPropertiesφ
7207⟨a, b | aaaba=bb⟩Can Inf
8504⟨a, b | aaaba=bab⟩Can Inf
9670⟨a, b | aabababba=1⟩Grp Inf18
9850⟨a, b | abababba=b⟩Can Inf
91174⟨a, b | aaaba=baab⟩Can Inf
115942⟨a, b | abbbba=babbb⟩Can Inf

Other submonoids of anti-isomorphic group

6 unique, 6 total

Σ#PresentationProperties
7174⟨a, b | aaabba=b⟩Can Inf
8362⟨a, b | aaababa=b⟩Can Inf
9765⟨a, b | aaabaaba=b⟩Can Inf
101612⟨a, b | aaabaaaba=b⟩Can Inf
102742⟨a, b | baaab=aaaba⟩Can Inf
113430⟨a, b | aaabaaaaba=b⟩Can Inf