#3512 ⟨a, b | aa=1, ababb=bb⟩

Up:Monoid enumeration
Prev:#3508 ⟨a, b | aa=1, ababa=bb⟩
Next:#3516 ⟨a, b | aa=1, abbab=bb⟩

Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-isomorphic instances

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. a2 ⇒ 1 [1]
2. b3 ⇒ b2 [4]
3. bab2 ⇒ ab2 [3]
# ab:aa=1,ababb=bb ab - -
aa=1
bbb=bb
babb=abb

Isomorphic instances

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

12 total

Σ#PresentationMapping
93669⟨a, b | aa=1, babb=abb⟩φ(a) = a, φ(b) = b
1127013⟨a, b | aa=1, aaababb=bb⟩φ(a) = a, φ(b) = b
1127094⟨a, b | aa=1, abaaabb=bb⟩φ(a) = a, φ(b) = b
1127110⟨a, b | aa=1, ababaab=bb⟩φ(a) = a, φ(b) = b
1127577⟨a, b | aa=1, aababb=abb⟩φ(a) = a, φ(b) = b
1127648⟨a, b | aa=1, ababba=bba⟩φ(a) = a, φ(b) = b
1127705⟨a, b | aa=1, baaabb=abb⟩φ(a) = a, φ(b) = b
1128077⟨a, b | aa=1, aaabb=babb⟩φ(a) = a, φ(b) = b
1128151⟨a, b | aa=1, abaab=babb⟩φ(a) = a, φ(b) = b
1128169⟨a, b | aa=1, ababb=aabb⟩φ(a) = a, φ(b) = b
1128175⟨a, b | aa=1, ababb=baab⟩φ(a) = a, φ(b) = b
1128178⟨a, b | aa=1, ababb=bbaa⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

5 total

Σ#PresentationMapping
1127064⟨a, b | aa=1, aabbaba=bb⟩φ(a) = a, φ(b) = b
1127594⟨a, b | aa=1, aabbab=bba⟩φ(a) = a, φ(b) = b
1127716⟨a, b | aa=1, baabab=bba⟩φ(a) = a, φ(b) = b
1128121⟨a, b | aa=1, aabba=bbab⟩φ(a) = a, φ(b) = b
1128188⟨a, b | aa=1, abbab=abba⟩φ(a) = a, φ(b) = b