#2157 ⟨a, b | aaabaaa=bab⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. a3ba3 ⇒ bab [1]
2. bab2a3 ⇒ a3b2ab [2]
3. (ba)3a2 ⇒ a2(ab)3 [3]
4. baba2ba3 ⇒ a(a2b)2ab [4]
# ab:aaabaaa=bab ab
aaabaaa=bab
babbaaa=aaabbab
bababaaa=aaababab
babaabaaa=aaabaabab

Other submonoids of same group

5 unique, 5 total

Σ#PresentationDescriptionRelated
9776⟨a, b | aaabbaaa=b⟩Infinite cancellative non-commutative monoid
9900⟨a, b | aaabaaa=bb⟩Infinite cancellative non-commutative monoid
101624⟨a, b | aaababaaa=b⟩Infinite cancellative non-commutative monoid
113442⟨a, b | aaabaabaaa=b⟩Infinite cancellative non-commutative monoid
115018⟨a, b | aaabaaa=baab⟩Infinite cancellative non-commutative monoid