#2912 ⟨a, b | aaabaaabbba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances
  5. 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 [11]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [10]
5. a4 ⇒ c [2]
6. ba3ba ⇒ d(bc)2 [24]
7. bcba3 ⇒ cba3b [21]
8. b3c ⇒ aba3b2 [15]
9. ba3b2d ⇒ a3db3 [12]
10. b3a ⇒ adb2cb [34]
11. ba3b2a ⇒ db(bc)2 [33]
12. bcba2cba ⇒ cba3d(bc)2 [27]
13. ba3b3 ⇒ d [3]
14. bcba2cb2d ⇒ cba2b3 [26]
15. bcba2cb2a ⇒ cba3db(bc)2 [38]
16. b2cba2ba ⇒ a3b2d(bc)2 [32]
17. bcba2cb3 ⇒ cba3d [25]
18. b2cba2b2d ⇒ a3b2a3db3 [31]
19. b2cba2b2a ⇒ a3b2db(bc)2 [37]
20. b2cba2b3 ⇒ a3b2d [30]
# ab:aaabaaabbba=1 reversed:cda/b aaaa=c,baaabbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
baaaba=dbcbc
bcbaaa=cbaaab
bbbc=abaaabb
baaabbd=aaadbbb
bbba=adbbcb
baaabba=dbbcbc
bcbaacba=cbaaadbcbc
baaabbb=d
bcbaacbbd=cbaabbb
bcbaacbba=cbaaadbbcbc
bbcbaaba=aaabbdbcbc
bcbaacbbb=cbaaad
bbcbaabbd=aaabbaaadbbb
bbcbaabba=aaabbdbbcbc
bbcbaabbb=aaabbd

Other submonoids of same group

1 unique, 1 total

Σ#PresentationProperties
113678⟨a, b | aabbbabbba=b⟩Can Inf

Isomorphic instances

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

4 total

Σ#PresentationMapping
112980⟨a, b | aaabbbaaaab=1⟩φ(a) = a, φ(b) = b
113026⟨a, b | aabaaabbbaa=1⟩φ(a) = a, φ(b) = b
113135⟨a, b | aabbbaaaaba=1⟩φ(a) = a, φ(b) = b
113159⟨a, b | aabbbbabbba=1⟩φ(a) = b, φ(b) = a

Anti-isomorphic instances

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

3 total

Σ#PresentationMapping
112981⟨a, b | aaabbbaaaba=1⟩φ(a) = a, φ(b) = b
113016⟨a, b | aabaaaabbba=1⟩φ(a) = a, φ(b) = b
113151⟨a, b | aabbbabbbba=1⟩φ(a) = b, φ(b) = a