#2214 ⟨a, b | ba=ab, aabb=a⟩

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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. a2b2 ⇒ a 
# ab:ba=ab,aabb=a ab
ba=ab
aabb=a

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.

15 total

Σ#PresentationMapping
92215⟨a, b | ba=ab, abab=a⟩φ(a) = a, φ(b) = b
92216⟨a, b | ba=ab, abba=a⟩φ(a) = a, φ(b) = b
92217⟨a, b | ba=ab, abba=b⟩φ(a) = b, φ(b) = a
104735⟨a, b | aabb=a, baab=a⟩φ(a) = a, φ(b) = b
104743⟨a, b | abab=a, baab=a⟩φ(a) = a, φ(b) = b
104745⟨a, b | abab=a, baba=a⟩φ(a) = a, φ(b) = b
104747⟨a, b | abba=a, baab=a⟩φ(a) = a, φ(b) = b
1112939⟨a, b | aba=aab, aabb=b⟩φ(a) = b, φ(b) = a
1112943⟨a, b | aba=aab, abab=b⟩φ(a) = b, φ(b) = a
1112945⟨a, b | aba=aab, abba=b⟩φ(a) = b, φ(b) = a
1112950⟨a, b | aba=aab, baab=a⟩φ(a) = a, φ(b) = b
1112952⟨a, b | aba=aab, baba=a⟩φ(a) = a, φ(b) = b
1113050⟨a, b | baa=aab, aabb=a⟩φ(a) = a, φ(b) = b
1113052⟨a, b | baa=aab, abab=a⟩φ(a) = a, φ(b) = b
1113058⟨a, b | baa=aab, baab=a⟩φ(a) = a, φ(b) = b