#1320 ⟨a, b | aaaababbba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances
  5. 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 [13]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [12]
5. a5 ⇒ c [2]
6. bcba ⇒ cbab [22]
7. baba4 ⇒ d(bc)2 [24]
8. b3c ⇒ a4bab2 [17]
9. bab2d ⇒ adb3 [14]
10. b3ac ⇒ a4bab2a [19]
11. bab2ad ⇒ adb3a [15]
12. b3a2c ⇒ a4bab2a2 [27]
13. bab2a2d ⇒ adb3a2 [26]
14. b3a3c ⇒ a4bab2a3 [30]
15. bab2a3d ⇒ adb3a3 [28]
16. b3a4 ⇒ a4db2cb [32]
17. bab2a4 ⇒ db(bc)2 [29]
18. bab3 ⇒ d [3]
# ab:aaaababbba=1 reversed:cda/b aaaaa=c,babbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaa=c
bcba=cbab
babaaaa=dbcbc
bbbc=aaaababb
babbd=adbbb
bbbac=aaaababba
babbad=adbbba
bbbaac=aaaababbaa
babbaad=adbbbaa
bbbaaac=aaaababbaaa
babbaaad=adbbbaaa
bbbaaaa=aaaadbbcb
babbaaaa=dbbcbc
babbb=d

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
102510⟨a, b | aababa=bbbb⟩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
101362⟨a, b | aaababbbaa=1⟩φ(a) = a, φ(b) = b
101471⟨a, b | aabbbbbaba=1⟩φ(a) = b, φ(b) = a
101541⟨a, b | abbbaaaaab=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.

3 total

Σ#PresentationMapping
101332⟨a, b | aaaabbbaba=1⟩φ(a) = a, φ(b) = b
101381⟨a, b | aaabbbabaa=1⟩φ(a) = a, φ(b) = b
101436⟨a, b | aababbbbba=1⟩φ(a) = b, φ(b) = a