#569 ⟨a, b | aaa=a, bab=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. c2 ⇒ a2
  2. a3 ⇒ a
  3. a2c ⇒ c
  4. ca2 ⇒ c
  5. ba ⇒ aca
  6. bc ⇒ a
  7. ab ⇒ c
  8. cb ⇒ cac 
# ab:aaa=a,bab=a ac/b ab=c frequency:2/2
cc=aa
aaa=a
aac=c
caa=c
ba=aca
bc=a
ab=c
cb=cac

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.

8 total

Σ#PresentationMapping
106266⟨a, b | aaa=a, baaab=a⟩φ(a) = a, φ(b) = b
106507⟨a, b | aba=b, ababb=b⟩φ(a) = b, φ(b) = a
106511⟨a, b | aba=b, abbba=b⟩φ(a) = b, φ(b) = a
106519⟨a, b | aba=b, babab=b⟩φ(a) = b, φ(b) = a
106785⟨a, b | aba=b, abbb=ab⟩φ(a) = b, φ(b) = a
106793⟨a, b | aba=b, babb=ba⟩φ(a) = b, φ(b) = a
106801⟨a, b | aaa=a, bab=aaa⟩φ(a) = a, φ(b) = b
106841⟨a, b | aba=b, bbb=aba⟩φ(a) = b, φ(b) = a