#5056 ⟨a, b | aaa=ab, abbb=a⟩

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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. a7 ⇒ a [2]
2. ab ⇒ a3 [1]
# ab:aaa=ab,abbb=a a/b
aaaaaaa=a
ab=aaa

Isomorphic instances

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

6 total

Σ#PresentationMapping
1115447⟨a, b | aaa=ab, aaabb=a⟩φ(a) = a, φ(b) = b
1115451⟨a, b | aaa=ab, aabab=a⟩φ(a) = a, φ(b) = b
1115453⟨a, b | aaa=ab, aabba=a⟩φ(a) = a, φ(b) = b
1115459⟨a, b | aaa=ab, abaab=a⟩φ(a) = a, φ(b) = b
1115461⟨a, b | aaa=ab, ababa=a⟩φ(a) = a, φ(b) = b
1115465⟨a, b | aaa=ab, abbaa=a⟩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.

2 total

Σ#PresentationMapping
1114488⟨a, b | aaab=b, aabbb=b⟩φ(a) = b, φ(b) = a
1114500⟨a, b | aaab=b, abbab=b⟩φ(a) = b, φ(b) = a