#3599 ⟨a, b, c | bb=aa, cc=ab⟩

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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. b2 ⇒ a2 [1]
2. c2 ⇒ ab [2]
3. ba2 ⇒ a2b [3]
4. cab ⇒ abc [4]
5. ca3 ⇒ abcb [5]
# abc:bb=aa,cc=ab abc - -
bb=aa
cc=ab
baa=aab
cab=abc
caaa=abcb

Other submonoids of same group

2 unique, 9 total

Σ#PresentationPropertiesφ
82183⟨a, b, c | aabb=1, bcac=1⟩Grp Inf7
83495⟨a, b, c | bb=aa, cac=b⟩Can Inf