#2869 ⟨a, b | aaaababbbba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. Anti-isomorphic instances

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 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 [21]
7. baba4 ⇒ d(bc)2 [23]
8. bab2a4 ⇒ db(bc)2 [25]
9. b4c ⇒ a4bab3 [17]
10. bab3d ⇒ adb4 [14]
11. b4ac ⇒ a4bab3a [19]
12. bab3ad ⇒ adb4a [15]
13. b4a2c ⇒ a4bab3a2 [28]
14. bab3a2d ⇒ adb4a2 [27]
15. b4a3c ⇒ a4bab3a3 [31]
16. bab3a3d ⇒ adb4a3 [29]
17. b4a4 ⇒ a4db3cb [33]
18. bab3a4 ⇒ db3cbc [30]
19. bab4 ⇒ d [3]
# ab:aaaababbbba=1 reversed:cda/b aaaaa=c,babbbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaa=c
bcba=cbab
babaaaa=dbcbc
babbaaaa=dbbcbc
bbbbc=aaaababbb
babbbd=adbbbb
bbbbac=aaaababbba
babbbad=adbbbba
bbbbaac=aaaababbbaa
babbbaad=adbbbbaa
bbbbaaac=aaaababbbaaa
babbbaaad=adbbbbaaa
bbbbaaaa=aaaadbbbcb
babbbaaaa=dbbbcbc
babbbb=d

Isomorphic instances

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

3 total

Σ#PresentationMapping
112951⟨a, b | aaababbbbaa=1⟩φ(a) = a, φ(b) = b
113000⟨a, b | aaabbbbbaba=1⟩φ(a) = b, φ(b) = a
113302⟨a, b | abbbbaaaaab=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.

4 total

Σ#PresentationMapping
112894⟨a, b | aaaabbbbaba=1⟩φ(a) = a, φ(b) = b
112953⟨a, b | aaababbbbba=1⟩φ(a) = b, φ(b) = a
112995⟨a, b | aaabbbbabaa=1⟩φ(a) = a, φ(b) = b
113092⟨a, b | aababbbbbaa=1⟩φ(a) = b, φ(b) = a