#2922 ⟨a, b | aaabaabbaba=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. ad ⇒ da [8]
2. da3 ⇒ 1 [9]
3. ca4b ⇒ da2 [22]
4. bac ⇒ d2a2 [12]
5. cac ⇒ ab2d [10]
6. ca3c ⇒ da(ab)2 [23]
7. ca4c ⇒ a(a2b)2d2a2 [40]
8. ca5c ⇒ ba4bda [32]
9. ba2b2 ⇒ dca3 [16]
10. b2ab ⇒ da2c [11]
11. ba4ba2b ⇒ ca4 [29]
12. baba4b ⇒ aca2 [25]
13. b2c ⇒ da2cbab [14]
14. ba2bc ⇒ dca7ba2bd2a2 [41]
15. ba2bdc ⇒ dca5b2d [28]
16. b2a2c ⇒ da2caba4bda [37]
17. ba4ba2c ⇒ ca8ba2bd2a2 [42]
18. b2dac ⇒ da2ca2b2d [15]
19. baba3c ⇒ aca(ab)2 [27]
20. ba4ba3c ⇒ ca(a4b)2da [35]
21. ba2bda2c ⇒ dca3bab [19]
22. ba4bda2c ⇒ ca6b2d [36]
23. baba4c ⇒ aca6ba2bd2a2 [46]
24. baba5c ⇒ aca3ba4bda [43]
# ab:aaabaabbaba=1 reversed:ad/bc abbab=c,abac=d morph:5/0,4/0
ad=da
daaa=1
caaaab=daa
bac=ddaa
cac=abbd
caaac=daabab
caaaac=aaabaabddaa
caaaaac=baaaabda
baabb=dcaaa
bbab=daac
baaaabaab=caaaa
babaaaab=acaa
bbc=daacbab
baabc=dcaaaaaaabaabddaa
baabdc=dcaaaaabbd
bbaac=daacabaaaabda
baaaabaac=caaaaaaaabaabddaa
bbdac=daacaabbd
babaaac=acaabab
baaaabaaac=caaaaabaaaabda
baabdaac=dcaaabab
baaaabdaac=caaaaaabbd
babaaaac=acaaaaaabaabddaa
babaaaaac=acaaabaaaabda

Other submonoids of same group

3 unique, 3 total

Σ#PresentationProperties
9824⟨a, b | aabbbaba=b⟩Can Inf
9955⟨a, b | aabbaba=bb⟩Can Inf
113790⟨a, b | ababbbabba=b⟩Can Inf

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationProperties
102506⟨a, b | aababa=babb⟩Can Inf

Isomorphic instances

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

3 total

Σ#PresentationMapping
113044⟨a, b | aabaabbabaa=1⟩φ(a) = a, φ(b) = daaab
113115⟨a, b | aabbabaaaab=1⟩φ(a) = a, φ(b) = daaab
113265⟨a, b | ababbbbabba=1⟩φ(a) = daaab, 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
112942⟨a, b | aaababbaaba=1⟩φ(a) = a, φ(b) = abdaa
113180⟨a, b | abaaaababba=1⟩φ(a) = a, φ(b) = abdaa
113277⟨a, b | abbaabaaaab=1⟩φ(a) = a, φ(b) = abdaa