#9785 ⟨a, b | aa=1, babbbab=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. b2 ⇒ c
  2. cb ⇒ bc
  3. a2 ⇒ 1
  4. babc ⇒ bcab
  5. bac2 ⇒ bcac
  6. cabc ⇒ c2ab
  7. cac2 ⇒ c2ac
  8. c(ab)2 ⇒ (ba)2c
  9. cabac ⇒ b 
# ab:aa=1,babbbab=b bca bb=c frequency:2/0
bb=c
cb=bc
aa=1
babc=bcab
bacc=bcac
cabc=ccab
cacc=ccac
cabab=babac
cabac=b

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
109793⟨a, b | aa=1, bbababb=b⟩φ(a) = a, φ(b) = b