#2918 ⟨a, b | aaabaababba=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 [5]
2. da2 ⇒ 1 [6]
3. cb ⇒ d2 [7]
4. ba4c ⇒ 1 [18]
5. c2 ⇒ dbab [9]
6. ca2c ⇒ d2ab2a4 [23]
7. ca3c ⇒ d2ba4ba2 [33]
8. ca4c ⇒ ba2ba [19]
9. bab2 ⇒ a2cd2 [12]
10. ba(ab)2 ⇒ c [2]
11. ba4ba2b ⇒ a4cda [42]
12. b2a4b ⇒ a3cd [28]
13. babc ⇒ a2cdbab [15]
14. ba2bac ⇒ ca(ab)2 [8]
15. baba2c ⇒ a2cd2ab2a4 [44]
16. ba4ba2c ⇒ a4c(ab)2 [36]
17. baba3c ⇒ a2cd2ba4ba2 [45]
18. ba2ba3c ⇒ cab2a4 [24]
19. ba2ba5c ⇒ ca3(aba)2 [21]
20. ba4ba5c ⇒ a4cdaba4ba2 [49]
21. b2a6c ⇒ a3cdab2a4 [47]
22. ba4ba6c ⇒ a4ca(a2b)2a [37]
23. b2a7c ⇒ a3cdba4ba2 [48]
24. b2a8c ⇒ a3c(a2b)2a [38]
# ab:aaabaababba=1 reversed:ad/bc baabab=c,aacb=d morph:6/0,4/0
ad=da
daa=1
cb=dd
baaaac=1
cc=dbab
caac=ddabbaaaa
caaac=ddbaaaabaa
caaaac=baaba
babb=aacdd
baabab=c
baaaabaab=aaaacda
bbaaaab=aaacd
babc=aacdbab
baabac=caabab
babaac=aacddabbaaaa
baaaabaac=aaaacabab
babaaac=aacddbaaaabaa
baabaaac=cabbaaaa
baabaaaaac=caaaabaaba
baaaabaaaaac=aaaacdabaaaabaa
bbaaaaaac=aaacdabbaaaa
baaaabaaaaaac=aaaacaaabaaba
bbaaaaaaac=aaacdbaaaabaa
bbaaaaaaaac=aaacaabaaba

Other submonoids of same group

2 unique, 2 total

Σ#PresentationProperties
9947⟨a, b | aababba=bb⟩Can Inf
113786⟨a, b | ababbabbba=b⟩Can Inf

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationProperties
9811⟨a, b | aababbba=b⟩Can Inf
102508⟨a, b | aababa=bbab⟩Can Inf

Isomorphic instances

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

3 total

Σ#PresentationMapping
113038⟨a, b | aabaababbaa=1⟩φ(a) = a, φ(b) = daab
113074⟨a, b | aababbaaaab=1⟩φ(a) = a, φ(b) = daab
113271⟨a, b | abbaaaabaab=1⟩φ(a) = a, φ(b) = daab

Anti-isomorphic instances

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

3 total

Σ#PresentationMapping
112968⟨a, b | aaabbabaaba=1⟩φ(a) = a, φ(b) = abda
113182⟨a, b | abaaaabbaba=1⟩φ(a) = a, φ(b) = abda
113259⟨a, b | ababbabbbba=1⟩φ(a) = abda, φ(b) = a