#10016 ⟨a, b | aa=1, abbabb=bb⟩

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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. c2b ⇒ b3
  2. c3 ⇒ b2c
  3. b4 ⇒ b2
  4. b3c ⇒ bc
  5. b2cb ⇒ cb
  6. b2c2 ⇒ c2
  7. cb3 ⇒ cb
  8. cb2c ⇒ c2
  9. ab2 ⇒ bcb
  10. abc ⇒ bc2
  11. acb ⇒ b(cb)2
  12. ac2 ⇒ bcbc2
  13. bab ⇒ c
  14. cab ⇒ bac
  15. a2 ⇒ 1 
# ab:aa=1,abbabb=bb bc/a bab=c frequency:3/1
ccb=bbb
ccc=bbc
bbbb=bb
bbbc=bc
bbcb=cb
bbcc=cc
cbbb=cb
cbbc=cc
abb=bcb
abc=bcc
acb=bcbcb
acc=bcbcc
bab=c
cab=bac
aa=1

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
1010335⟨a, b | aa=1, bbabb=abb⟩φ(a) = a, φ(b) = b