#1642 ⟨a, b | aab=ba, bba=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. a4 ⇒ a
  2. ab ⇒ ba2
  3. b2a ⇒ a 
# ab:aab=ba,bba=a a/b
aaaa=a
ab=baa
bba=a

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

17 total

Σ#PresentationMapping
92065⟨a, b | aab=b, abba=b⟩φ(a) = b, φ(b) = a
105176⟨a, b | aab=ba, baab=a⟩φ(a) = a, φ(b) = b
1112251⟨a, b | aaab=ab, abba=b⟩φ(a) = b, φ(b) = a
1112385⟨a, b | aaba=ba, abba=b⟩φ(a) = b, φ(b) = a
1112440⟨a, b | aabb=aa, baab=a⟩φ(a) = a, φ(b) = b
1112558⟨a, b | abba=aa, baab=a⟩φ(a) = a, φ(b) = b
1114854⟨a, b | abba=b, ababb=b⟩φ(a) = b, φ(b) = a
1114866⟨a, b | abba=b, babab=b⟩φ(a) = b, φ(b) = a
1115683⟨a, b | aab=ba, aabab=a⟩φ(a) = a, φ(b) = b
1115693⟨a, b | aab=ba, ababa=a⟩φ(a) = a, φ(b) = b
1115713⟨a, b | aab=ba, babaa=a⟩φ(a) = a, φ(b) = b
1118973⟨a, b | aab=b, aaabba=b⟩φ(a) = b, φ(b) = a
1118997⟨a, b | aab=b, abaaba=b⟩φ(a) = b, φ(b) = a
1119529⟨a, b | aab=b, aabba=ab⟩φ(a) = b, φ(b) = a
1119577⟨a, b | aab=b, baaba=ab⟩φ(a) = b, φ(b) = a
1120062⟨a, b | aab=b, aaab=bba⟩φ(a) = b, φ(b) = a
1120097⟨a, b | aab=b, abba=aab⟩φ(a) = b, φ(b) = a