#4275 ⟨a, b | aaabb=1, aabba=1⟩

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  1. Properties
  2. Rewriting system
  3. 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. ca ⇒ ac [5]
2. cb ⇒ bc [9]
3. a3 ⇒ c [3]
4. b2a ⇒ ab2 [12]
5. b2c ⇒ 1 [8]
# ab:aaabb=1,aabba=1 abc aaa=c morph:3/0
ca=ac
cb=bc
aaa=c
bba=abb
bbc=1

Isomorphic instances

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

8 total

Σ#PresentationMapping
104280⟨a, b | aaabb=1, abbaa=1⟩φ(a) = a, φ(b) = b
104283⟨a, b | aaabb=1, baaab=1⟩φ(a) = a, φ(b) = b
104289⟨a, b | aaabb=1, bbaaa=1⟩φ(a) = a, φ(b) = b
104322⟨a, b | aabba=1, abbaa=1⟩φ(a) = a, φ(b) = b
104325⟨a, b | aabba=1, baaab=1⟩φ(a) = a, φ(b) = b
1112811⟨a, b | baa=aab, aabbb=1⟩φ(a) = b, φ(b) = a
1112816⟨a, b | baa=aab, abbba=1⟩φ(a) = b, φ(b) = a
1112819⟨a, b | baa=aab, baabb=1⟩φ(a) = b, φ(b) = a