#60 ⟨a, b | aaabba=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 [14]
4. cd ⇒ 1 [9]
5. da ⇒ ad [12]
6. db ⇒ bd [5]
7. dc ⇒ 1 [13]
8. a4 ⇒ c [2]
# ab:aaabba=1 abcd aaaa=c,bb=d magic:0
bb=d
ca=ac
cb=bc
cd=1
da=ad
db=bd
dc=1
aaaa=c

Other submonoids of same group

8 unique, 9 total

Σ#PresentationDescriptionRelated
693⟨a, b | abbba=b⟩Infinite cancellative non-commutative monoid
696⟨a, b | aaaa=bb⟩Infinite cancellative non-commutative monoid
6113⟨a, b | abba=bb⟩Infinite cancellative non-commutative monoid
6122⟨a, b | bab=aaa⟩Infinite cancellative non-commutative monoid
8404⟨a, b | abababa=b⟩Infinite cancellative non-commutative monoid1 iso
8549⟨a, b | ababa=bab⟩Infinite cancellative non-commutative monoid
102355⟨a, b | abbabba=bab⟩Infinite cancellative non-commutative monoid
102586⟨a, b | abaaba=baab⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

19 total

Σ#PresentationMapping
665⟨a, b | aabbaa=1⟩φ(a) = a, φ(b) = b
673⟨a, b | abbbba=1⟩φ(a) = b, φ(b) = a
8279⟨a, b | aaaababa=1⟩φ(a) = a, φ(b) = aaadb
8288⟨a, b | aaababaa=1⟩φ(a) = a, φ(b) = aaadb
8321⟨a, b | abaaaaab=1⟩φ(a) = a, φ(b) = aaadb
101293⟨a, b | aaaaabaaba=1⟩φ(a) = a, φ(b) = aaadbaaad
101310⟨a, b | aaaabaabaa=1⟩φ(a) = a, φ(b) = aaadbaaad
101344⟨a, b | aaabaabaaa=1⟩φ(a) = a, φ(b) = aaadbaaad
101391⟨a, b | aabaaaaaab=1⟩φ(a) = a, φ(b) = aaadaaadb
101409⟨a, b | aabaabbaab=1⟩φ(a) = bc, φ(b) = bba
101421⟨a, b | aababababa=1⟩φ(a) = b, φ(b) = bca
101442⟨a, b | aabbaabaab=1⟩φ(a) = bc, φ(b) = bba
101476⟨a, b | abaaaaaaba=1⟩φ(a) = a, φ(b) = aaadbaaad
101485⟨a, b | abaaababab=1⟩φ(a) = b, φ(b) = bca
101493⟨a, b | abaabaabba=1⟩φ(a) = bc, φ(b) = bab
101499⟨a, b | abaabbaaba=1⟩φ(a) = bc, φ(b) = bab
101506⟨a, b | ababaaabab=1⟩φ(a) = b, φ(b) = bca
101511⟨a, b | abababaaab=1⟩φ(a) = b, φ(b) = bca
101539⟨a, b | abbabbabba=1⟩φ(a) = bab, φ(b) = bc