#182 ⟨a, b | aabbaa=b⟩

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Contents

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

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. b3a2 ⇒ a2b3 [2]
2. a2b2a2 ⇒ b [1]
3. bab2a2 ⇒ a2b2ab [3]
# ab:aabbaa=b ab - -
bbbaa=aabbb
aabbaa=b
babbaa=aabbab

Other submonoids of same group

11 unique, 22 total

Σ#PresentationPropertiesφ
7214⟨a, b | aabaa=bb⟩Can Inf
8378⟨a, b | aababaa=b⟩Can Inf
8519⟨a, b | aabaa=bab⟩Can Inf
9672⟨a, b | aababbaba=1⟩Grp Inf10
9796⟨a, b | aabaabaa=b⟩Can Inf
9854⟨a, b | ababbaba=b⟩Can Inf1
91204⟨a, b | aabaa=baab⟩Can Inf
101670⟨a, b | aabaaabaa=b⟩Can Inf
102743⟨a, b | baaab=aabaa⟩Can Inf
114843⟨a, b | ababbaba=bab⟩Can Inf
115943⟨a, b | abbbba=bbabb⟩Can Inf

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

1 total

Σ#PresentationMapping
113540⟨a, b | aabaaaabaa=b⟩φ(a) = a, φ(b) = bb