#67 ⟨a, b | aabbba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. 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. ca ⇒ ac [5]
2. cb ⇒ bc [13]
3. cd ⇒ 1 [9]
4. da ⇒ ad [11]
5. db ⇒ bd [6]
6. dc ⇒ 1 [12]
7. a3 ⇒ c [2]
8. b3 ⇒ d [3]
# ab:aabbba=1 abcd aaa=c,bbb=d magic:0
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaa=c
bbb=d

Other submonoids of same group

5 unique, 6 total

Σ#PresentationPropertiesφ
6124⟨a, b | bbb=aaa⟩Can Inf
7229⟨a, b | ababa=bb⟩Can Inf
8410⟨a, b | abbabba=b⟩Can Inf1
91115⟨a, b | abaaba=bab⟩Can Inf
115304⟨a, b | abaaaba=baab⟩Can Inf

Isomorphic instances

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

8 total

Σ#PresentationMapping
9635⟨a, b | aaabababa=1⟩φ(a) = a, φ(b) = aadb
9640⟨a, b | aaabbaaab=1⟩φ(a) = aad, φ(b) = aaba
9658⟨a, b | aabaaabba=1⟩φ(a) = aad, φ(b) = aaba
9668⟨a, b | aabababaa=1⟩φ(a) = a, φ(b) = aadb
9677⟨a, b | aabbaaaba=1⟩φ(a) = aad, φ(b) = aaba
9697⟨a, b | abaaaabab=1⟩φ(a) = a, φ(b) = aadb
9710⟨a, b | ababaaaab=1⟩φ(a) = a, φ(b) = aadb
9729⟨a, b | abbbabbba=1⟩φ(a) = aaba, φ(b) = aad