#2940 ⟨a, b | aaabababbba=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 [39]
3. cb ⇒ bc [5]
4. db ⇒ bd [32]
5. b3 ⇒ c [2]
6. a(ba)2c ⇒ (ba)2ca [41]
7. abacad ⇒ b2da(ba)2 [42]
8. (ab)3c ⇒ (ba)2cab [43]
9. abacabd ⇒ b2d(ab)3 [44]
10. (ab)3bc ⇒ (ba)2cab2 [45]
11. abacab2d ⇒ b2d(ab)3b [47]
12. abaca2d ⇒ b2da2(ba)2 [48]
13. a4b ⇒ bdaca3 [52]
14. abaca2bd ⇒ b2da(ab)3 [49]
15. aca3b2 ⇒ b2a4c [57]
16. abaca2b2d ⇒ b2da(ab)3b [58]
17. abaca3d ⇒ b2da3(ba)2 [59]
18. abaca3bd ⇒ b2da2(ab)3 [61]
19. a2(ab)3b ⇒ baca4 [38]
20. abaca4 ⇒ b2d [37]
21. aca4cad ⇒ b2a3b2da(ba)2 [63]
22. aca4cabd ⇒ b2a3b2d(ab)3 [64]
23. aca4cab2d ⇒ b2a3b2d(ab)3b [65]
24. aca4ca2d ⇒ b2a3b2da2(ba)2 [66]
25. aca4ca2bd ⇒ b2a3b2da(ab)3 [67]
26. aca4ca2b2d ⇒ b2a3b2da(ab)3b [68]
27. (aca3)2d ⇒ b2a3b2da3(ba)2 [69]
28. (aca3)2bd ⇒ b2a3b2da2(ab)3 [70]
29. a(ca4)2 ⇒ b2a3b2d [62]
# ab:aaabababbba=1 reversed:cdb/a bbb=c,aaaababa=d magic:1
dc=1
cd=1
cb=bc
db=bd
bbb=c
ababac=babaca
abacad=bbdababa
abababc=babacab
abacabd=bbdababab
abababbc=babacabb
abacabbd=bbdabababb
abacaad=bbdaababa
aaaab=bdacaaa
abacaabd=bbdaababab
acaaabb=bbaaaac
abacaabbd=bbdaabababb
abacaaad=bbdaaababa
abacaaabd=bbdaaababab
aaabababb=bacaaaa
abacaaaa=bbd
acaaaacad=bbaaabbdababa
acaaaacabd=bbaaabbdababab
acaaaacabbd=bbaaabbdabababb
acaaaacaad=bbaaabbdaababa
acaaaacaabd=bbaaabbdaababab
acaaaacaabbd=bbaaabbdaabababb
acaaaacaaad=bbaaabbdaaababa
acaaaacaaabd=bbaaabbdaaababab
acaaaacaaaa=bbaaabbd

Other submonoids of same group

1 unique, 1 total

Σ#PresentationProperties
102174⟨a, b | aaababa=bbb⟩Can Inf

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationProperties
113993⟨a, b | aaabababa=bb⟩Can Inf

Isomorphic instances

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

3 total

Σ#PresentationMapping
113071⟨a, b | aabababbbaa=1⟩φ(a) = a, φ(b) = babacaaaab
113157⟨a, b | aabbbbababa=1⟩φ(a) = babacaaaab, φ(b) = a
113260⟨a, b | ababbbaaaab=1⟩φ(a) = a, φ(b) = babacaaaab

Anti-isomorphic instances

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

3 total

Σ#PresentationMapping
112987⟨a, b | aaabbbababa=1⟩φ(a) = a, φ(b) = abbabacaaa
113073⟨a, b | aabababbbba=1⟩φ(a) = abbabacaaa, φ(b) = a
113264⟨a, b | ababbbbaaab=1⟩φ(a) = abbabacaaa, φ(b) = a