#9749 ⟨a, b | aa=1, abbabbb=b⟩

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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
  2. cac2 ⇒ ac
  3. c(ac)2 ⇒ c
  4. b(ac)2 ⇒ b
  5. cb ⇒ bc
  6. cab ⇒ abac2ac
  7. b2 ⇒ c 
# ab:aa=1,abbabbb=b ac/b bb=c frequency:2/1
aa=1
cacc=ac
cacac=c
bacac=b
cb=bc
cab=abaccac
bb=c

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.

1 total

Σ#PresentationMapping
1010058⟨a, b | aa=1, bbabbb=ab⟩φ(a) = a, φ(b) = b