#3602 ⟨a, b, c | bb=ac, cb=aa⟩

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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. ac ⇒ b2 [1]
2. cb ⇒ a2 [2]
3. a3 ⇒ b3 [3]
4. ab3 ⇒ b3a [5]
5. a2b2 ⇒ b3c [4]
# abc:bb=ac,cb=aa bac - -
ac=bb
cb=aa
aaa=bbb
abbb=bbba
aabb=bbbc

Other submonoids of same group

4 unique, 31 total

Σ#PresentationPropertiesφ
82084⟨a, b, c | aaab=1, bccc=1⟩Grp Inf26
82854⟨a, b, c | aaa=b, ccc=b⟩Can Inf1
82991⟨a, b, c | aab=c, bcc=a⟩Can Inf
86089⟨a, b, c | ab=c, bcc=aa⟩Can Inf