#2176 ⟨a, b | ab=aa, aaaa=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. ab ⇒ a2
  2. a4 ⇒ a 
# ab:ab=aa,aaaa=a ab
ab=aa
aaaa=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.

32 total

Σ#PresentationMapping
92178⟨a, b | ab=aa, aaab=a⟩φ(a) = a, φ(b) = b
92180⟨a, b | ab=aa, aaba=a⟩φ(a) = a, φ(b) = b
92182⟨a, b | ab=aa, aabb=a⟩φ(a) = a, φ(b) = b
92184⟨a, b | ab=aa, abaa=a⟩φ(a) = a, φ(b) = b
92186⟨a, b | ab=aa, abab=a⟩φ(a) = a, φ(b) = b
92188⟨a, b | ab=aa, abba=a⟩φ(a) = a, φ(b) = b
92190⟨a, b | ab=aa, abbb=a⟩φ(a) = a, φ(b) = b
104614⟨a, b | aaaa=a, aaab=a⟩φ(a) = a, φ(b) = b
104651⟨a, b | aaab=a, aabb=a⟩φ(a) = a, φ(b) = b
104655⟨a, b | aaab=a, abab=a⟩φ(a) = a, φ(b) = b
104657⟨a, b | aaab=a, abba=a⟩φ(a) = a, φ(b) = b
104702⟨a, b | aaba=a, abab=a⟩φ(a) = a, φ(b) = b
1112880⟨a, b | aab=aaa, aaaa=a⟩φ(a) = a, φ(b) = b
1112882⟨a, b | aab=aaa, aaab=a⟩φ(a) = a, φ(b) = b
1112884⟨a, b | aab=aaa, aaba=a⟩φ(a) = a, φ(b) = b
1112886⟨a, b | aab=aaa, aabb=a⟩φ(a) = a, φ(b) = b
1112888⟨a, b | aab=aaa, abaa=a⟩φ(a) = a, φ(b) = b
1112890⟨a, b | aab=aaa, abab=a⟩φ(a) = a, φ(b) = b
1112914⟨a, b | aba=aaa, aaab=a⟩φ(a) = a, φ(b) = b
1112920⟨a, b | aba=aaa, abab=a⟩φ(a) = a, φ(b) = b
1112998⟨a, b | abb=aab, aaab=a⟩φ(a) = a, φ(b) = b
1113002⟨a, b | abb=aab, aabb=a⟩φ(a) = a, φ(b) = b
1113005⟨a, b | abb=aab, abab=a⟩φ(a) = a, φ(b) = b
1113014⟨a, b | abb=aba, aaab=a⟩φ(a) = a, φ(b) = b
1113022⟨a, b | abb=aba, abab=a⟩φ(a) = a, φ(b) = b
1113026⟨a, b | abb=aba, abbb=a⟩φ(a) = a, φ(b) = b
1113031⟨a, b | abb=aba, baab=b⟩φ(a) = b, φ(b) = a
1113033⟨a, b | abb=aba, baba=b⟩φ(a) = b, φ(b) = a
1113035⟨a, b | abb=aba, babb=b⟩φ(a) = b, φ(b) = a
1113037⟨a, b | abb=aba, bbaa=b⟩φ(a) = b, φ(b) = a
1113039⟨a, b | abb=aba, bbab=b⟩φ(a) = b, φ(b) = a
1113041⟨a, b | abb=aba, bbba=b⟩φ(a) = b, φ(b) = a