#5663 ⟨a, b, c | aa=b, aaa=cc⟩

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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. a3 ⇒ c2 [2]
2. c2a ⇒ ac2 [3]
3. b ⇒ a2 [1]
# abc:aa=b,aaa=cc ac/b - -
aaa=cc
cca=acc
b=aa

Other submonoids of same group

12 unique, 172 total

Σ#PresentationPropertiesφ
7279⟨a, b, c | aaa=b, cbc=1⟩Grp Inf146
7543⟨a, b, c | ba=ac, cb=a⟩Can Inf
7555⟨a, b, c | bb=ac, cb=a⟩Can Inf4
7558⟨a, b, c | bb=ac, cc=a⟩Can Inf2
7937⟨a, b, c | aa=b, cbc=a⟩Can Inf2
71042⟨a, b, c | ab=c, bcc=a⟩Can Inf2
83045⟨a, b, c | aba=c, abc=b⟩Can Inf2
83051⟨a, b, c | aba=c, bab=c⟩Can Inf
83071⟨a, b, c | abc=b, bca=c⟩Can Inf2
83595⟨a, b, c | ba=ac, cb=ac⟩Can Inf
86019⟨a, b, c | ab=c, aba=bc⟩Can Inf
86071⟨a, b, c | ab=c, bac=ca⟩Can Inf

Isomorphic instances

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

1 total

Σ#PresentationMapping
85991⟨a, b, c | ab=c, aaa=bb⟩φ(a) = a, φ(b) = c, φ(c) = ac