#2199 ⟨a, b, c | aabc=1, acba=1⟩

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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. ad ⇒ da [10]
2. bd ⇒ db [8]
3. bc ⇒ d [3]
4. cd ⇒ dc [9]
5. cb ⇒ d [7]
6. da2 ⇒ 1 [11]
7. ba2 ⇒ a2b [16]
8. ca2 ⇒ a2c [17]
# abc:aabc=1,acba=1 dabc bc=d morph:2/0
ad=da
bd=db
bc=d
cd=dc
cb=d
daa=1
baa=aab
caa=aac

Other submonoids of same group

8 unique, 11 total

Σ#PresentationPropertiesφ
7533⟨a, b, c | ba=ab, cc=a⟩Can Inf
82976⟨a, b, c | aab=c, baa=c⟩Can Inf2
83072⟨a, b, c | abc=b, cba=b⟩Can Inf
83431⟨a, b, c | ba=ab, cac=b⟩Can Inf
83587⟨a, b, c | ba=ab, cc=ab⟩Can Inf1
83592⟨a, b, c | ba=ac, ca=ab⟩Can Inf
83596⟨a, b, c | ba=ac, cc=bb⟩Can Inf
86088⟨a, b, c | ab=c, bca=cc⟩Can Inf

Isomorphic instances

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

5 total

Σ#PresentationMapping
82226⟨a, b, c | aabc=1, cbaa=1⟩φ(a) = a, φ(b) = dadaaab, φ(c) = c
82294⟨a, b, c | abbc=1, cbba=1⟩φ(a) = cdada, φ(b) = a, φ(c) = aab
82295⟨a, b, c | abca=1, acba=1⟩φ(a) = a, φ(b) = dadaaab, φ(c) = c
83195⟨a, b, c | ba=ab, cabc=1⟩φ(a) = dadaaab, φ(b) = c, φ(c) = a
84604⟨a, b, c | abc=1, cbba=b⟩φ(a) = cda, φ(b) = a, φ(c) = aab