#172 ⟨a, b | aaa=1, bbbb=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. a3 ⇒ 1
  2. b4 ⇒ 1 
# ab:aaa=1,bbbb=1 ab
aaa=1
bbbb=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.

15 total

Σ#PresentationMapping
91359⟨a, b | aaab=b, bbbb=1⟩φ(a) = a, φ(b) = b
92442⟨a, b | aaa=1, abbbb=a⟩φ(a) = a, φ(b) = b
107223⟨a, b | aaa=1, aaabbbb=1⟩φ(a) = a, φ(b) = b
107236⟨a, b | aaa=1, aabbbba=1⟩φ(a) = a, φ(b) = b
107263⟨a, b | aaa=1, baaabbb=1⟩φ(a) = a, φ(b) = b
107274⟨a, b | aaa=1, bbaaabb=1⟩φ(a) = a, φ(b) = b
108090⟨a, b | aaa=1, bbbb=aaa⟩φ(a) = a, φ(b) = b
1116567⟨a, b | aaaa=1, aaaabbb=1⟩φ(a) = b, φ(b) = a
1116574⟨a, b | aaaa=1, aaabbba=1⟩φ(a) = b, φ(b) = a
1116586⟨a, b | aaaa=1, aabbbaa=1⟩φ(a) = b, φ(b) = a
1116613⟨a, b | aaaa=1, baaaabb=1⟩φ(a) = b, φ(b) = a
1117642⟨a, b | aaaa=1, aabbb=aa⟩φ(a) = b, φ(b) = a
1117661⟨a, b | aaaa=1, abbba=aa⟩φ(a) = b, φ(b) = a
1122246⟨a, b | aaa=1, aabbbb=aa⟩φ(a) = a, φ(b) = b
1122285⟨a, b | aaa=1, abbbba=aa⟩φ(a) = a, φ(b) = b