#2318 ⟨a, b | abaabba=bab⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

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. ab ⇒ c [2]
2. (ac)2bc ⇒ c2b [6]
3. cacba ⇒ bc [4]
4. c2b2 ⇒ a(cac)2bc [9]
5. bcb ⇒ cacbc [5]
6. c2bcacbc ⇒ a(cac)2bc2b [10]
7. bc2acbc ⇒ cacbc2b [7]
8. c(cba)2 ⇒ (ac)2b2c [8]
# ab:abaabba=bab reversed:ca/b ab=c morph:2/0
ab=c
acacbc=ccb
cacba=bc
ccbb=acaccacbc
bcb=cacbc
ccbcacbc=acaccacbccb
bccacbc=cacbccb
ccbacba=acacbbc

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
101782⟨a, b | ababaabba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

5 unique, 5 total

Σ#PresentationDescriptionRelated
9838⟨a, b | abaaabba=b⟩Infinite cancellative non-commutative monoid
91100⟨a, b | aabbba=bab⟩Infinite cancellative non-commutative monoid
102758⟨a, b | baabb=ababa⟩Infinite cancellative non-commutative monoid
113708⟨a, b | abaaaababa=b⟩Infinite cancellative non-commutative monoid
114850⟨a, b | ababbbba=bab⟩Infinite cancellative non-commutative monoid