#5293 ⟨a, b | aba=bb, bbbb=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. b3 ⇒ c2
  2. bc2 ⇒ b
  3. c2b ⇒ b
  4. c3 ⇒ c
  5. ab ⇒ b2cb
  6. ac ⇒ b2
  7. ba ⇒ c
  8. ca ⇒ cb2c 
# ab:aba=bb,bbbb=b bc/a ba=c frequency:2/1
bbb=cc
bcc=b
ccb=b
ccc=c
ab=bbcb
ac=bb
ba=c
ca=cbbc

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.

2 total

Σ#PresentationMapping
1115926⟨a, b | aba=bb, ababb=b⟩φ(a) = a, φ(b) = b
1115938⟨a, b | aba=bb, babab=b⟩φ(a) = a, φ(b) = b