#563 ⟨a, b | aaa=a, aab=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. a3 ⇒ a 
# ab:aaa=a,aab=a ab
ab=aa
aaa=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.

35 total

Σ#PresentationMapping
8584⟨a, b | aab=a, abb=a⟩φ(a) = a, φ(b) = b
8630⟨a, b | ab=aa, aaa=a⟩φ(a) = a, φ(b) = b
8632⟨a, b | ab=aa, aab=a⟩φ(a) = a, φ(b) = b
8634⟨a, b | ab=aa, aba=a⟩φ(a) = a, φ(b) = b
8636⟨a, b | ab=aa, abb=a⟩φ(a) = a, φ(b) = b
104167⟨a, b | abb=aba, bab=b⟩φ(a) = b, φ(b) = a
104169⟨a, b | abb=aba, bba=b⟩φ(a) = b, φ(b) = a
104197⟨a, b | bab=baa, bba=b⟩φ(a) = b, φ(b) = a
106240⟨a, b | aaa=a, aaaab=a⟩φ(a) = a, φ(b) = b
106320⟨a, b | aab=a, aaaab=a⟩φ(a) = a, φ(b) = b
106322⟨a, b | aab=a, aaaba=a⟩φ(a) = a, φ(b) = b
106326⟨a, b | aab=a, aabaa=a⟩φ(a) = a, φ(b) = b
106332⟨a, b | aab=a, aabbb=a⟩φ(a) = a, φ(b) = b
106334⟨a, b | aab=a, abaaa=a⟩φ(a) = a, φ(b) = b
106340⟨a, b | aab=a, ababb=a⟩φ(a) = a, φ(b) = b
106344⟨a, b | aab=a, abbab=a⟩φ(a) = a, φ(b) = b
106346⟨a, b | aab=a, abbba=a⟩φ(a) = a, φ(b) = b
106448⟨a, b | aba=a, aaaab=a⟩φ(a) = a, φ(b) = b
106468⟨a, b | aba=a, abbab=a⟩φ(a) = a, φ(b) = b
106527⟨a, b | aaa=a, aaaa=ab⟩φ(a) = a, φ(b) = b
106529⟨a, b | aaa=a, aaab=aa⟩φ(a) = a, φ(b) = b
106598⟨a, b | aab=a, aaaa=aa⟩φ(a) = a, φ(b) = b
106603⟨a, b | aab=a, aaab=ab⟩φ(a) = a, φ(b) = b
106607⟨a, b | aab=a, aaba=ab⟩φ(a) = a, φ(b) = b
106610⟨a, b | aab=a, aabb=aa⟩φ(a) = a, φ(b) = b
106615⟨a, b | aab=a, abaa=ab⟩φ(a) = a, φ(b) = b
106618⟨a, b | aab=a, abab=aa⟩φ(a) = a, φ(b) = b
106622⟨a, b | aab=a, abba=aa⟩φ(a) = a, φ(b) = b
106627⟨a, b | aab=a, abbb=ab⟩φ(a) = a, φ(b) = b
106632⟨a, b | aab=a, baaa=ba⟩φ(a) = a, φ(b) = b
106644⟨a, b | aab=a, babb=ba⟩φ(a) = a, φ(b) = b
106734⟨a, b | aba=a, aaba=ab⟩φ(a) = a, φ(b) = b
106741⟨a, b | aba=a, abab=aa⟩φ(a) = a, φ(b) = b
106798⟨a, b | aaa=a, aab=aaa⟩φ(a) = a, φ(b) = b
106810⟨a, b | aab=a, abb=aab⟩φ(a) = a, φ(b) = b