#2174 ⟨a, b, c | aabb=1, acca=1⟩

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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. ad ⇒ da [10]
2. bd ⇒ db [5]
3. b2 ⇒ d [3]
4. cd ⇒ dc [9]
5. c2 ⇒ d [8]
6. da2 ⇒ 1 [11]
7. ba2 ⇒ a2b [16]
8. ca2 ⇒ a2c [17]
# abc:aabb=1,acca=1 dabc bb=d morph:2/0
ad=da
bd=db
bb=d
cd=dc
cc=d
daa=1
baa=aab
caa=aac

Isomorphic instances

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

6 total

Σ#PresentationMapping
82182⟨a, b, c | aabb=1, bbcc=1⟩φ(a) = b, φ(b) = a, φ(c) = c
82186⟨a, b, c | aabb=1, caac=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82281⟨a, b, c | abba=1, acca=1⟩φ(a) = a, φ(b) = b, φ(c) = c
82285⟨a, b, c | abba=1, bccb=1⟩φ(a) = b, φ(b) = a, φ(c) = c
82287⟨a, b, c | abba=1, cbbc=1⟩φ(a) = b, φ(b) = a, φ(c) = c
83258⟨a, b, c | bb=aa, caac=1⟩φ(a) = b, φ(b) = c, φ(c) = a