#290 ⟨a, b | aaababba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group
  5. Isomorphic instances
  6. Anti-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. dc ⇒ 1 [12]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [11]
5. a4 ⇒ c [2]
6. b2c ⇒ a3bab [16]
7. babd ⇒ adb2 [13]
8. bcba ⇒ cbab [19]
9. b2ac ⇒ a3(ba)2 [18]
10. (ba)2d ⇒ adb2a [14]
11. b2a2c ⇒ a3baba2 [22]
12. baba2d ⇒ adb2a2 [21]
13. b2a3 ⇒ a3dbcb [25]
14. baba3 ⇒ d(bc)2 [23]
15. bab2 ⇒ d [3]
# ab:aaababba=1 reversed:cda/b aaaa=c,babb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
bbc=aaabab
babd=adbb
bcba=cbab
bbac=aaababa
babad=adbba
bbaac=aaababaa
babaad=adbbaa
bbaaa=aaadbcb
babaaa=dbcbc
babb=d

Other submonoids of same group

6 unique, 6 total

Σ#PresentationDescriptionRelated
7254⟨a, b | aaba=bbb⟩Infinite cancellative non-commutative monoid
8478⟨a, b | ababba=bb⟩Infinite cancellative non-commutative monoid
9863⟨a, b | abbabbba=b⟩Infinite cancellative non-commutative monoid
91263⟨a, b | ababa=babb⟩Infinite cancellative non-commutative monoid
114796⟨a, b | abaababa=bab⟩Infinite cancellative non-commutative monoid
115405⟨a, b | abbabba=babb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
7186⟨a, b | aabbba=b⟩Infinite cancellative non-commutative monoid
9804⟨a, b | aabababa=b⟩Infinite cancellative non-commutative monoid
113560⟨a, b | aabaabaaba=b⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

9 total

Σ#PresentationMapping
8308⟨a, b | aababbaa=1⟩φ(a) = a, φ(b) = aaadab
8335⟨a, b | abbaaaab=1⟩φ(a) = a, φ(b) = aaadab
101366⟨a, b | aaabbaaaba=1⟩φ(a) = aaad, φ(b) = aaaba
101396⟨a, b | aabaaaabba=1⟩φ(a) = aaad, φ(b) = aaaba
101544⟨a, b | abbbabbbba=1⟩φ(a) = aabaa, φ(b) = aaad
112849⟨a, b | aaaabaababa=1⟩φ(a) = a, φ(b) = aaadabaaad
112916⟨a, b | aaabaababaa=1⟩φ(a) = a, φ(b) = aaadabaaad
113052⟨a, b | aababaaaaab=1⟩φ(a) = a, φ(b) = aaadaaadab
113173⟨a, b | abaaaaabaab=1⟩φ(a) = a, φ(b) = aaadaaadab

Anti-isomorphic instances

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

10 total

Σ#PresentationMapping
8294⟨a, b | aaabbaba=1⟩φ(a) = a, φ(b) = aaadab
8334⟨a, b | ababbbba=1⟩φ(a) = aaadab, φ(b) = a
101342⟨a, b | aaabaaabba=1⟩φ(a) = aaad, φ(b) = aabaa
101365⟨a, b | aaabbaaaab=1⟩φ(a) = aaad, φ(b) = aaaab
101400⟨a, b | aabaaabbaa=1⟩φ(a) = aaad, φ(b) = aabaa
101438⟨a, b | aabbaaaaba=1⟩φ(a) = aaad, φ(b) = aabaa
112857⟨a, b | aaaababaaba=1⟩φ(a) = a, φ(b) = aaadabaaad
112930⟨a, b | aaababaabaa=1⟩φ(a) = a, φ(b) = aaadabaaad
113174⟨a, b | abaaaaababa=1⟩φ(a) = a, φ(b) = aaadabaaad
113200⟨a, b | abaabaaaaab=1⟩φ(a) = a, φ(b) = aaadaaadab