#27144 ⟨a, b | aa=1, abbabba=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. b6 ⇒ b2
  2. cb4 ⇒ c
  3. b4c ⇒ c
  4. ab2 ⇒ b2cb2
  5. b2a ⇒ c
  6. c2 ⇒ b2cb2
  7. cb2c ⇒ b2
  8. ca ⇒ b2
  9. cba ⇒ cb3c
  10. ac ⇒ cb2
  11. abc ⇒ b(bc)2
  12. a2 ⇒ 1 
# ab:aa=1,abbabba=bb b/ca bba=c frequency:3/0
bbbbbb=bb
cbbbb=c
bbbbc=c
abb=bbcbb
bba=c
cc=bbcbb
cbbc=bb
ca=bb
cba=cbbbc
ac=cbb
abc=bbcbc
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.

2 total

Σ#PresentationMapping
1127672⟨a, b | aa=1, abbabb=bba⟩φ(a) = a, φ(b) = b
1128281⟨a, b | aa=1, bbabb=abba⟩φ(a) = a, φ(b) = b