#2888 ⟨a, b | aa=a, babab=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. a2 ⇒ a
  2. ba ⇒ ab
  3. ab3 ⇒ a 
# ab:aa=a,babab=a ab
aa=a
ba=ab
abbb=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.

28 total

Σ#PresentationMapping
105180⟨a, b | aab=ba, babb=a⟩φ(a) = a, φ(b) = b
105184⟨a, b | aab=ba, bbab=a⟩φ(a) = a, φ(b) = b
105264⟨a, b | aba=ab, babb=a⟩φ(a) = a, φ(b) = b
108624⟨a, b | aa=a, baabab=a⟩φ(a) = a, φ(b) = b
108899⟨a, b | aa=a, babab=aa⟩φ(a) = a, φ(b) = b
1112299⟨a, b | aaab=bb, aaba=b⟩φ(a) = b, φ(b) = a
1112407⟨a, b | aaba=bb, abaa=b⟩φ(a) = b, φ(b) = a
1114608⟨a, b | aaba=b, aaabb=b⟩φ(a) = b, φ(b) = a
1114620⟨a, b | aaba=b, abaab=b⟩φ(a) = b, φ(b) = a
1114622⟨a, b | aaba=b, ababa=b⟩φ(a) = b, φ(b) = a
1114626⟨a, b | aaba=b, abbaa=b⟩φ(a) = b, φ(b) = a
1115651⟨a, b | aab=ab, babab=a⟩φ(a) = a, φ(b) = b
1115687⟨a, b | aab=ba, aabbb=a⟩φ(a) = a, φ(b) = b
1115695⟨a, b | aab=ba, ababb=a⟩φ(a) = a, φ(b) = b
1115699⟨a, b | aab=ba, abbab=a⟩φ(a) = a, φ(b) = b
1115701⟨a, b | aab=ba, abbba=a⟩φ(a) = a, φ(b) = b
1115711⟨a, b | aab=ba, baabb=a⟩φ(a) = a, φ(b) = b
1115715⟨a, b | aab=ba, babab=a⟩φ(a) = a, φ(b) = b
1115717⟨a, b | aab=ba, babba=a⟩φ(a) = a, φ(b) = b
1115725⟨a, b | aab=ba, bbaba=a⟩φ(a) = a, φ(b) = b
1115729⟨a, b | aab=ba, bbbaa=a⟩φ(a) = a, φ(b) = b
1115879⟨a, b | aba=ab, baabb=a⟩φ(a) = a, φ(b) = b
1115883⟨a, b | aba=ab, babab=a⟩φ(a) = a, φ(b) = b
1115885⟨a, b | aba=ab, babba=a⟩φ(a) = a, φ(b) = b
1124152⟨a, b | aa=a, baaabab=a⟩φ(a) = a, φ(b) = b
1124156⟨a, b | aa=a, baabaab=a⟩φ(a) = a, φ(b) = b
1124695⟨a, b | aa=a, baabab=aa⟩φ(a) = a, φ(b) = b
1125234⟨a, b | aa=a, babab=aaa⟩φ(a) = a, φ(b) = b