#617 ⟨a, b | aaaababba=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 [14]
2. cd ⇒ 1 [9]
3. ca ⇒ ac [6]
4. da ⇒ ad [12]
5. a5 ⇒ c [2]
6. b2c ⇒ a4bab [17]
7. babd ⇒ adb2 [15]
8. bcba ⇒ cbab [20]
9. b2ac ⇒ a4(ba)2 [19]
10. (ba)2d ⇒ adb2a [13]
11. b2a2c ⇒ a4baba2 [23]
12. baba2d ⇒ adb2a2 [22]
13. b2a3c ⇒ a4baba3 [26]
14. baba3d ⇒ adb2a3 [24]
15. b2a4 ⇒ a4dbcb [28]
16. baba4 ⇒ d(bc)2 [25]
17. bab2 ⇒ d [3]
# ab:aaaababba=1 reversed:cda/b aaaaa=c,babb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaa=c
bbc=aaaabab
babd=adbb
bcba=cbab
bbac=aaaababa
babad=adbba
bbaac=aaaababaa
babaad=adbbaa
bbaaac=aaaababaaa
babaaad=adbbaaa
bbaaaa=aaaadbcb
babaaaa=dbcbc
babb=d

Other submonoids of same group

4 unique, 4 total

Σ#PresentationDescriptionRelated
91128⟨a, b | ababba=bbb⟩Infinite cancellative non-commutative monoid
102084⟨a, b | abbabbba=bb⟩Infinite cancellative non-commutative monoid
113829⟨a, b | abbbabbbba=b⟩Infinite cancellative non-commutative monoid
115363⟨a, b | abababa=babb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

3 unique, 3 total

Σ#PresentationDescriptionRelated
8392⟨a, b | aabbbba=b⟩Infinite cancellative non-commutative monoid
8590⟨a, b | babb=aaaa⟩Infinite cancellative non-commutative monoid
113593⟨a, b | aababababa=b⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

2 total

Σ#PresentationMapping
9637⟨a, b | aaababbaa=1⟩φ(a) = a, φ(b) = aaaadab
9721⟨a, b | abbaaaaab=1⟩φ(a) = a, φ(b) = aaaadab

Anti-isomorphic instances

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

3 total

Σ#PresentationMapping
9621⟨a, b | aaaabbaba=1⟩φ(a) = a, φ(b) = aaaadab
9643⟨a, b | aaabbabaa=1⟩φ(a) = a, φ(b) = aaaadab
9720⟨a, b | ababbbbba=1⟩φ(a) = aaaadab, φ(b) = a