#639 ⟨a, b | aaababbba=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. bcba ⇒ cbab [21]
7. baba3 ⇒ d(bc)2 [23]
8. b3c ⇒ a3bab2 [16]
9. bab2d ⇒ adb3 [13]
10. b3ac ⇒ a3bab2a [18]
11. bab2ad ⇒ adb3a [14]
12. b3a2c ⇒ a3bab2a2 [26]
13. bab2a2d ⇒ adb3a2 [25]
14. b3a3 ⇒ a3db2cb [29]
15. bab2a3 ⇒ db(bc)2 [27]
16. bab3 ⇒ d [3]
# ab:aaababbba=1 reversed:cda/b aaaa=c,babbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
bcba=cbab
babaaa=dbcbc
bbbc=aaababb
babbd=adbbb
bbbac=aaababba
babbad=adbbba
bbbaac=aaababbaa
babbaad=adbbbaa
bbbaaa=aaadbbcb
babbaaa=dbbcbc
babbb=d

Other submonoids of same group

2 unique, 2 total

Σ#PresentationDescriptionRelated
91076⟨a, b | aababa=bbb⟩Infinite cancellative non-commutative monoid
114313⟨a, b | ababbabba=bb⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
101965⟨a, b | aabababa=bb⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

3 total

Σ#PresentationMapping
9673⟨a, b | aababbbaa=1⟩φ(a) = a, φ(b) = b
9691⟨a, b | aabbbbaba=1⟩φ(a) = b, φ(b) = a
9728⟨a, b | abbbaaaab=1⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

2 total

Σ#PresentationMapping
9648⟨a, b | aaabbbaba=1⟩φ(a) = a, φ(b) = b
9675⟨a, b | aababbbba=1⟩φ(a) = b, φ(b) = a