#151 ⟨a, b | ba=ab, aaa=1⟩

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Properties

Complete 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
  1. ba ⇒ ab
  2. a3 ⇒ 1 
# ab:ba=ab,aaa=1 ab
ba=ab
aaa=1

Staircase diagram

Right Cayley graph (truncated)

Other isomorphic instances

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

11 total

Σ#PresentationMapping
8741⟨a, b | aaa=1, aaba=b⟩φ(a) = a, φ(b) = b
91311⟨a, b | bab=abb, bbb=1⟩φ(a) = b, φ(b) = a
91313⟨a, b | bba=abb, bbb=1⟩φ(a) = b, φ(b) = a
107757⟨a, b | aaa=1, aaaab=ba⟩φ(a) = a, φ(b) = b
107760⟨a, b | aaa=1, aaaba=ab⟩φ(a) = a, φ(b) = b
107768⟨a, b | aaa=1, aabaa=ab⟩φ(a) = a, φ(b) = b
1121653⟨a, b | aaa=1, aaaaaba=b⟩φ(a) = a, φ(b) = b
1121657⟨a, b | aaa=1, aaaabaa=b⟩φ(a) = a, φ(b) = b
1123266⟨a, b | aaa=1, aaba=aaab⟩φ(a) = a, φ(b) = b
1123270⟨a, b | aaa=1, abaa=aaab⟩φ(a) = a, φ(b) = b
1123271⟨a, b | aaa=1, abaa=aaba⟩φ(a) = a, φ(b) = b