#1410 ⟨a, b | aabaabbaba=1⟩

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Quick links

  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 to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. ad ⇒ da [5]
2. da2 ⇒ 1 [6]
3. cab ⇒ d2a [7]
4. ba3c ⇒ da [17]
5. cac ⇒ dab2 [9]
6. ca2c ⇒ d2(ab)2a2 [21]
7. ca3c ⇒ ba2bda [18]
8. ca4c ⇒ dba3ba [31]
9. ba2b2 ⇒ c [2]
10. b2ab ⇒ acd [11]
11. ba(a2b)2 ⇒ a2ca [27]
12. baba3b ⇒ a3cda [37]
13. ba2bc ⇒ ca2b2 [8]
14. b2ac ⇒ acb2 [15]
15. ba2bac ⇒ cbaba2 [22]
16. b2a2c ⇒ acdbaba2 [24]
17. (ba2)2c ⇒ ca(a2b)2da [20]
18. ba3ba2c ⇒ a2ca3b2 [29]
19. b2a4c ⇒ acdaba3ba [35]
20. baba4c ⇒ a3cd(ab)2a2 [39]
21. ba3ba4c ⇒ a2ca4ba2bda [33]
22. baba5c ⇒ a3c(a2b)2da [41]
23. ba3ba5c ⇒ a2c(a2ba)2 [34]
24. baba6c ⇒ a3cba3ba [36]
# ab:aabaabbaba=1 reversed:ad/bc baabb=c,acab=d morph:5/0,4/0
ad=da
daa=1
cab=dda
baaac=da
cac=dabb
caac=ddababaa
caaac=baabda
caaaac=dbaaaba
baabb=c
bbab=acd
baaabaab=aaca
babaaab=aaacda
baabc=caabb
bbac=acbb
baabac=cbabaa
bbaac=acdbabaa
baabaac=caaabaabda
baaabaac=aacaaabb
bbaaaac=acdabaaaba
babaaaac=aaacdababaa
baaabaaaac=aacaaaabaabda
babaaaaac=aaacaabaabda
baaabaaaaac=aacaabaaaba
babaaaaaac=aaacbaaaba

Other submonoids of same group

3 unique, 3 total

Σ#PresentationDescriptionRelated
8386⟨a, b | aabbaba=b⟩Infinite cancellative non-commutative monoid
8591⟨a, b | babb=aaba⟩Infinite cancellative non-commutative monoid
101690⟨a, b | aababaaba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationDescriptionRelated
102610⟨a, b | ababba=babb⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

2 total

Σ#PresentationMapping
101447⟨a, b | aabbabaaab=1⟩φ(a) = a, φ(b) = daab
101523⟨a, b | ababbbabba=1⟩φ(a) = daab, 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
101427⟨a, b | aababbaaba=1⟩φ(a) = a, φ(b) = daab
101486⟨a, b | abaaababba=1⟩φ(a) = a, φ(b) = daab
101531⟨a, b | abbaabaaab=1⟩φ(a) = a, φ(b) = daab