#2437 ⟨a, b | aaa=1, ababb=b⟩

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  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. a3 ⇒ 1 [1]
2. bab2 ⇒ a2b [3]
3. b(ab)2 ⇒ b [6]
4. baba2b ⇒ ab [5]
# ab:aaa=1,ababb=b ab
aaa=1
babb=aab
babab=b
babaab=ab

Isomorphic instances

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

3 total

Σ#PresentationMapping
108083⟨a, b | aaa=1, babb=aab⟩φ(a) = a, φ(b) = b
1122232⟨a, b | aaa=1, aababb=ab⟩φ(a) = a, φ(b) = b
1122267⟨a, b | aaa=1, ababba=ba⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1122301⟨a, b | aaa=1, baabab=ba⟩φ(a) = a, φ(b) = b