#5066 ⟨a, b | aaa=ab, bbaa=a

Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-isomorphic instances

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1
1
#RuleProof
1. a6 ⇒ a [4]
2. ab ⇒ a3 [1]
3. b2a ⇒ a5 [5]
# ab:aaa=ab,bbaa=a a/b
aaaaaa=a
ab=aaa
bba=aaaaa

Isomorphic instances

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

4 total

Σ#PresentationMapping
1112405a, b | aaba=bb, aabb=bφ(a) = b, φ(b) = a
1112417a, b | aaba=bb, baab=bφ(a) = b, φ(b) = a
1112419a, b | aaba=bb, baba=bφ(a) = b, φ(b) = a
1112423a, b | aaba=bb, bbaa=bφ(a) = b, φ(b) = a

Anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1114697a, b | aabb=a, baaaa=aφ(a) = a, φ(b) = b