#5219 ⟨a, b | aab=bb, bbba=b

Quick links

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-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. b6 ⇒ b [6]
2. ba ⇒ b4 [7]
3. a2b ⇒ b2 [1]
# ab:aab=bb,bbba=b b/a
bbbbbb=b
ba=bbbb
aab=bb

Isomorphic instances

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

5 total

Σ#PresentationMapping
1114459a, b | aaab=a, bbaab=aφ(a) = b, φ(b) = a
1114461a, b | aaab=a, bbaba=aφ(a) = b, φ(b) = a
1114587a, b | aaba=a, bbaab=aφ(a) = b, φ(b) = a
1115750a, b | aab=bb, aabba=bφ(a) = a, φ(b) = b
1115774a, b | aab=bb, baaba=bφ(a) = a, φ(b) = b

Anti-isomorphic instances

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

2 total

Σ#PresentationMapping
1114575a, b | aaba=a, baabb=aφ(a) = b, φ(b) = a
1115762a, b | aab=bb, abbaa=bφ(a) = a, φ(b) = b