#5293 ⟨a, b | aba=bb, bbbb=b

Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances

Properties

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
#RuleProof
1. b3 ⇒ c2 [5]
2. bc2 ⇒ b [8]
3. c2b ⇒ b [9]
4. c3 ⇒ c [11]
5. ab ⇒ b2cb [10]
6. ac ⇒ b2 [4]
7. ba ⇒ c [3]
8. ca ⇒ cb2c [12]
# ab:aba=bb,bbbb=b bc/a ba=c morph:2/1
bbb=cc
bcc=b
ccb=b
ccc=c
ab=bbcb
ac=bb
ba=c
ca=cbbc

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

2 total

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