#64 ⟨a, b | aa=1, aaaa=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. a2 ⇒ 1 
# ab:aa=1,aaaa=1 ab
aa=1

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.

42 total

Σ#PresentationMapping
684⟨a, b | aa=1, aaa=a⟩φ(a) = a, φ(b) = 1
687⟨a, b | aa=1, aab=b⟩φ(a) = a, φ(b) = 1
8491⟨a, b | aaa=a, aaaa=1⟩φ(a) = a, φ(b) = 1
81024⟨a, b | aa=1, aaaaaa=1⟩φ(a) = a, φ(b) = 1
81096⟨a, b | aa=1, aaaaa=a⟩φ(a) = a, φ(b) = 1
81099⟨a, b | aa=1, aaaab=b⟩φ(a) = a, φ(b) = 1
81105⟨a, b | aa=1, aabaa=b⟩φ(a) = a, φ(b) = 1
81168⟨a, b | aa=1, aaaa=aa⟩φ(a) = a, φ(b) = 1
81172⟨a, b | aa=1, aaab=ab⟩φ(a) = a, φ(b) = 1
81177⟨a, b | aa=1, aaba=ba⟩φ(a) = a, φ(b) = 1
81182⟨a, b | aa=1, aabb=bb⟩φ(a) = a, φ(b) = 1
81196⟨a, b | aa=1, baab=bb⟩φ(a) = a, φ(b) = 1
81246⟨a, b | aa=1, baa=aab⟩φ(a) = a, φ(b) = 1
105422⟨a, b | aaaa=1, aaaaaa=1⟩φ(a) = a, φ(b) = 1
105966⟨a, b | aaa=a, aaaaaa=1⟩φ(a) = a, φ(b) = 1
109384⟨a, b | aa=1, aaaaaaaa=1⟩φ(a) = a, φ(b) = 1
109656⟨a, b | aa=1, aaaaaaa=a⟩φ(a) = a, φ(b) = 1
109659⟨a, b | aa=1, aaaaaab=b⟩φ(a) = a, φ(b) = 1
109665⟨a, b | aa=1, aaaabaa=b⟩φ(a) = a, φ(b) = 1
109928⟨a, b | aa=1, aaaaaa=aa⟩φ(a) = a, φ(b) = 1
109932⟨a, b | aa=1, aaaaab=ab⟩φ(a) = a, φ(b) = 1
109937⟨a, b | aa=1, aaaaba=ba⟩φ(a) = a, φ(b) = 1
109942⟨a, b | aa=1, aaaabb=bb⟩φ(a) = a, φ(b) = 1
109944⟨a, b | aa=1, aaabaa=ab⟩φ(a) = a, φ(b) = 1
109962⟨a, b | aa=1, aabaab=bb⟩φ(a) = a, φ(b) = 1
109973⟨a, b | aa=1, aabbaa=bb⟩φ(a) = a, φ(b) = 1
1010030⟨a, b | aa=1, baaaab=bb⟩φ(a) = a, φ(b) = 1
1010200⟨a, b | aa=1, aaaaa=aaa⟩φ(a) = a, φ(b) = 1
1010207⟨a, b | aa=1, aaaab=aab⟩φ(a) = a, φ(b) = 1
1010210⟨a, b | aa=1, aaaab=baa⟩φ(a) = a, φ(b) = 1
1010216⟨a, b | aa=1, aaaba=aba⟩φ(a) = a, φ(b) = 1
1010225⟨a, b | aa=1, aaabb=abb⟩φ(a) = a, φ(b) = 1
1010231⟨a, b | aa=1, aabaa=aab⟩φ(a) = a, φ(b) = 1
1010241⟨a, b | aa=1, aabab=bab⟩φ(a) = a, φ(b) = 1
1010250⟨a, b | aa=1, aabba=bba⟩φ(a) = a, φ(b) = 1
1010259⟨a, b | aa=1, aabbb=bbb⟩φ(a) = a, φ(b) = 1
1010263⟨a, b | aa=1, abaab=abb⟩φ(a) = a, φ(b) = 1
1010308⟨a, b | aa=1, baaab=bab⟩φ(a) = a, φ(b) = 1
1010317⟨a, b | aa=1, baabb=bbb⟩φ(a) = a, φ(b) = 1
1010478⟨a, b | aa=1, abaa=aaab⟩φ(a) = a, φ(b) = 1
1010505⟨a, b | aa=1, baab=aabb⟩φ(a) = a, φ(b) = 1
1010523⟨a, b | aa=1, bbaa=aabb⟩φ(a) = a, φ(b) = 1