#2823 ⟨a, b | aaaaababbba=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 [15]
2. cd ⇒ 1 [9]
3. ca ⇒ ac [6]
4. da ⇒ ad [13]
5. a6 ⇒ c [2]
6. bcba ⇒ cbab [26]
7. baba5 ⇒ d(bc)2 [28]
8. b3c ⇒ a5bab2 [18]
9. bab2d ⇒ adb3 [16]
10. b3ac ⇒ a5bab2a [20]
11. bab2ad ⇒ adb3a [14]
12. b3a2c ⇒ a5bab2a2 [30]
13. bab2a2d ⇒ adb3a2 [22]
14. b3a3c ⇒ a5bab2a3 [34]
15. bab2a3d ⇒ adb3a3 [32]
16. b3a4c ⇒ a5bab2a4 [37]
17. bab2a4d ⇒ adb3a4 [36]
18. b3a5 ⇒ a5db2cb [40]
19. bab2a5 ⇒ db(bc)2 [33]
20. bab3 ⇒ d [3]
# ab:aaaaababbba=1 reversed:cda/b aaaaaa=c,babbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaaa=c
bcba=cbab
babaaaaa=dbcbc
bbbc=aaaaababb
babbd=adbbb
bbbac=aaaaababba
babbad=adbbba
bbbaac=aaaaababbaa
babbaad=adbbbaa
bbbaaac=aaaaababbaaa
babbaaad=adbbbaaa
bbbaaaac=aaaaababbaaaa
babbaaaad=adbbbaaaa
bbbaaaaa=aaaaadbbcb
babbaaaaa=dbbcbc
babbb=d

Other submonoids of same group

1 unique, 1 total

Σ#PresentationProperties
115708⟨a, b | aababa=bbbbb⟩Can Inf

Isomorphic instances

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

4 total

Σ#PresentationMapping
112867⟨a, b | aaaababbbaa=1⟩φ(a) = a, φ(b) = b
112947⟨a, b | aaababbbaaa=1⟩φ(a) = a, φ(b) = b
113165⟨a, b | aabbbbbbaba=1⟩φ(a) = b, φ(b) = a
113295⟨a, b | abbbaaaaaab=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
112835⟨a, b | aaaaabbbaba=1⟩φ(a) = a, φ(b) = b
112888⟨a, b | aaaabbbabaa=1⟩φ(a) = a, φ(b) = b
113094⟨a, b | aababbbbbba=1⟩φ(a) = b, φ(b) = a