#601 ⟨a, b | aaaaaabba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. 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. b2 ⇒ d [3]
2. ca ⇒ ac [6]
3. cb ⇒ bc [17]
4. cd ⇒ 1 [9]
5. da ⇒ ad [19]
6. db ⇒ bd [5]
7. dc ⇒ 1 [16]
8. a7 ⇒ c [2]
# ab:aaaaaabba=1 abcd aaaaaaa=c,bb=d magic:0
bb=d
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaaaaa=c

Other submonoids of same group

7 unique, 7 total

Σ#PresentationDescriptionRelated
9866⟨a, b | abbbbbba=b⟩Infinite cancellative non-commutative monoid
9869⟨a, b | aaaaaaa=bb⟩Infinite cancellative non-commutative monoid
91002⟨a, b | abbbbba=bb⟩Infinite cancellative non-commutative monoid
91007⟨a, b | aaaaaa=bab⟩Infinite cancellative non-commutative monoid
91138⟨a, b | abbbba=bbb⟩Infinite cancellative non-commutative monoid
91146⟨a, b | aaaaa=baab⟩Infinite cancellative non-commutative monoid
91274⟨a, b | abbba=bbbb⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

8 total

Σ#PresentationMapping
9607⟨a, b | aaaaabbaa=1⟩φ(a) = a, φ(b) = b
9619⟨a, b | aaaabbaaa=1⟩φ(a) = a, φ(b) = b
9730⟨a, b | abbbbbbba=1⟩φ(a) = b, φ(b) = a
112787⟨a, b | aaaaaaababa=1⟩φ(a) = a, φ(b) = aaaaaadb
112797⟨a, b | aaaaaababaa=1⟩φ(a) = a, φ(b) = aaaaaadb
112817⟨a, b | aaaaababaaa=1⟩φ(a) = a, φ(b) = aaaaaadb
112855⟨a, b | aaaababaaaa=1⟩φ(a) = a, φ(b) = aaaaaadb
113169⟨a, b | abaaaaaaaab=1⟩φ(a) = a, φ(b) = aaaaaadb