#6633 ⟨a, b, c | aa=1, aabca=c⟩

Up:Monoid enumeration
Prev:#6632 ⟨a, b, c | aa=1, aabca=b⟩
Next:#6638 ⟨a, b, c | aa=1, aabcc=b⟩

Contents

  1. Properties
  2. Rewriting system
  3. 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. a2 ⇒ 1 [1]
2. bc ⇒ ca [3]
# abc:aa=1,aabca=c acb - -
aa=1
bc=ca

Isomorphic instances

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

4 total

Σ#PresentationMapping
87126⟨a, b, c | aa=1, aaba=cb⟩φ(a) = a, φ(b) = c, φ(c) = b
87139⟨a, b, c | aa=1, aabc=ca⟩φ(a) = a, φ(b) = b, φ(c) = c
87175⟨a, b, c | aa=1, abca=ac⟩φ(a) = a, φ(b) = b, φ(c) = c
87629⟨a, b, c | aa=1, aca=abc⟩φ(a) = a, φ(b) = b, φ(c) = c