#6177 ⟨a, b, c | aa=1, abcacb=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. a2 ⇒ 1 [1]
2. babd ⇒ ad(ab)2 [20]
3. cb ⇒ d [3]
4. babc ⇒ adaba [19]
5. dabd ⇒ ab [18]
6. dabc ⇒ a [17]
7. cadab ⇒ 1 [11]
8. bcad ⇒ a [5]
9. bcac ⇒ acada [9]
10. dcad ⇒ ca [6]
11. cad2 ⇒ abd(ca)2 [16]
12. (ca)2d ⇒ d(ca)2 [8]
# abc:aa=1,abcacb=1 ab/dc cb=d morph:2/0
aa=1
babd=adabab
cb=d
babc=adaba
dabd=ab
dabc=a
cadab=1
bcad=a
bcac=acada
dcad=ca
cadd=abdcaca
cacad=dcaca

Isomorphic instances

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

1 total

Σ#PresentationMapping
86768⟨a, b, c | aa=1, bcacb=a⟩φ(a) = a, φ(b) = b, φ(c) = c