#1707 ⟨a, b | aaaa=1, aabbb=1⟩

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Quick links

  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. ba2 ⇒ a2b [4]
2. b3 ⇒ a2 [3]
3. a4 ⇒ 1 [1]
# ab:aaaa=1,aabbb=1 ab
baa=aab
bbb=aa
aaaa=1

Isomorphic instances

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

18 total

Σ#PresentationMapping
91712⟨a, b | aaaa=1, abbba=1⟩φ(a) = a, φ(b) = b
91715⟨a, b | aaaa=1, baabb=1⟩φ(a) = a, φ(b) = b
1111102⟨a, b | aaaaa=a, aabbb=1⟩φ(a) = a, φ(b) = b
1111107⟨a, b | aaaaa=a, abbba=1⟩φ(a) = a, φ(b) = b
1111110⟨a, b | aaaaa=a, baabb=1⟩φ(a) = a, φ(b) = b
1111169⟨a, b | aaaab=b, aabbb=1⟩φ(a) = a, φ(b) = b
1111176⟨a, b | aaaab=b, abbba=1⟩φ(a) = a, φ(b) = b
1111181⟨a, b | aaaab=b, baabb=1⟩φ(a) = a, φ(b) = b
1111187⟨a, b | aaaab=b, bbaab=1⟩φ(a) = a, φ(b) = b
1111190⟨a, b | aaaab=b, bbbaa=1⟩φ(a) = a, φ(b) = b
1111328⟨a, b | aabaa=b, aabbb=1⟩φ(a) = a, φ(b) = b
1111334⟨a, b | aabaa=b, abbba=1⟩φ(a) = a, φ(b) = b
1111338⟨a, b | aabaa=b, baabb=1⟩φ(a) = a, φ(b) = b
1113800⟨a, b | abbba=1, bbbbbb=1⟩φ(a) = a, φ(b) = b
1117102⟨a, b | aaaa=1, aaabbb=a⟩φ(a) = a, φ(b) = b
1117114⟨a, b | aaaa=1, aabbba=a⟩φ(a) = a, φ(b) = b
1117122⟨a, b | aaaa=1, abaabb=a⟩φ(a) = a, φ(b) = b
1117130⟨a, b | aaaa=1, abbaab=a⟩φ(a) = a, φ(b) = b