#2799 ⟨a, b | aaaaaababba=1⟩

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Contents

  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:
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 [17]
2. cd ⇒ 1 [9]
3. ca ⇒ ac [6]
4. da ⇒ ad [14]
5. a7 ⇒ c [2]
6. b2c ⇒ a6bab [19]
7. babd ⇒ adb2 [15]
8. bcba ⇒ cbab [25]
9. b2ac ⇒ a6(ba)2 [21]
10. (ba)2d ⇒ adb2a [16]
11. b2a2c ⇒ a6baba2 [27]
12. baba2d ⇒ adb2a2 [23]
13. b2a3c ⇒ a6baba3 [30]
14. baba3d ⇒ adb2a3 [29]
15. b2a4c ⇒ a6baba4 [34]
16. baba4d ⇒ adb2a4 [32]
17. b2a5c ⇒ a6baba5 [37]
18. baba5d ⇒ adb2a5 [36]
19. b2a6 ⇒ a6dbcb [40]
20. baba6 ⇒ d(bc)2 [33]
21. bab2 ⇒ d [3]
# ab:aaaaaababba=1 reversed:cda/b aaaaaaa=c,babb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaaaaa=c
bbc=aaaaaabab
babd=adbb
bcba=cbab
bbac=aaaaaababa
babad=adbba
bbaac=aaaaaababaa
babaad=adbbaa
bbaaac=aaaaaababaaa
babaaad=adbbaaa
bbaaaac=aaaaaababaaaa
babaaaad=adbbaaaa
bbaaaaac=aaaaaababaaaaa
babaaaaad=adbbaaaaa
bbaaaaaa=aaaaaadbcb
babaaaaaa=dbcbc
babb=d

Other submonoids of same group

2 unique, 2 total

Σ#PresentationProperties
102371⟨a, b | aaaaaa=babb⟩Can Inf
115908⟨a, b | ababba=bbbbb⟩Can Inf

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationProperties
101746⟨a, b | aabbbbbba=b⟩Can Inf

Isomorphic instances

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

3 total

Σ#PresentationMapping
112821⟨a, b | aaaaababbaa=1⟩φ(a) = a, φ(b) = aaaaaadab
112863⟨a, b | aaaababbaaa=1⟩φ(a) = a, φ(b) = aaaaaadab
113269⟨a, b | abbaaaaaaab=1⟩φ(a) = a, φ(b) = aaaaaadab

Anti-isomorphic instances

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

4 total

Σ#PresentationMapping
112803⟨a, b | aaaaaabbaba=1⟩φ(a) = a, φ(b) = abaaaaaad
112829⟨a, b | aaaaabbabaa=1⟩φ(a) = a, φ(b) = abaaaaaad
112877⟨a, b | aaaabbabaaa=1⟩φ(a) = a, φ(b) = abaaaaaad
113268⟨a, b | ababbbbbbba=1⟩φ(a) = abaaaaaad, φ(b) = a