#5363 ⟨a, b | abababa=babb⟩

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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. cba ⇒ abc [5]
2. cb2 ⇒ a(ba)2c [6]
3. cab2 ⇒ babc [4]
4. bab2 ⇒ c [2]
5. a(ba)3 ⇒ c [3]
# ab:abababa=babb ac/b babb=c magic:0
cba=abc
cbb=ababac
cabb=babc
babb=c
abababa=c

Other submonoids of same group

4 unique, 9 total

Σ#PresentationPropertiesφ
9617⟨a, b | aaaababba=1⟩Grp Inf5
91128⟨a, b | ababba=bbb⟩Can Inf
102084⟨a, b | abbabbba=bb⟩Can Inf
113829⟨a, b | abbbabbbba=b⟩Can Inf

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationProperties
8392⟨a, b | aabbbba=b⟩Can Inf
8590⟨a, b | babb=aaaa⟩Can Inf
113593⟨a, b | aababababa=b⟩Can Inf