#664 ⟨a, b | aabaabbba=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. dc ⇒ 1 [10]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [9]
5. a3 ⇒ c [2]
6. ba2ba ⇒ d(bc)2 [23]
7. bcba2 ⇒ cba2b [20]
8. b3c ⇒ aba2b2 [14]
9. ba2b2d ⇒ a2db3 [11]
10. b3a ⇒ adb2cb [33]
11. ba2b2a ⇒ db(bc)2 [32]
12. b(cba)2 ⇒ cba2d(bc)2 [26]
13. ba2b3 ⇒ d [3]
14. bcbacb2d ⇒ cbab3 [25]
15. bcbacb2a ⇒ cba2db(bc)2 [36]
16. b2c(ba)2 ⇒ a2b2d(bc)2 [31]
17. bcbacb3 ⇒ cba2d [24]
18. b2cbab2d ⇒ a2b2a2db3 [30]
19. b2cbab2a ⇒ a2b2db(bc)2 [37]
20. b2cbab3 ⇒ a2b2d [29]
# ab:aabaabbba=1 reversed:cda/b aaa=c,baabbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
baaba=dbcbc
bcbaa=cbaab
bbbc=abaabb
baabbd=aadbbb
bbba=adbbcb
baabba=dbbcbc
bcbacba=cbaadbcbc
baabbb=d
bcbacbbd=cbabbb
bcbacbba=cbaadbbcbc
bbcbaba=aabbdbcbc
bcbacbbb=cbaad
bbcbabbd=aabbaadbbb
bbcbabba=aabbdbbcbc
bbcbabbb=aabbd

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
9820⟨a, b | aabbabba=b⟩Infinite cancellative non-commutative monoid

Other submonoids of anti-isomorphic group

2 unique, 2 total

Σ#PresentationDescriptionRelated
102041⟨a, b | abaababa=bb⟩Infinite cancellative non-commutative monoid
102587⟨a, b | abaaba=babb⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

6 total

Σ#PresentationMapping
9686⟨a, b | aabbbaaab=1⟩φ(a) = a, φ(b) = b
9689⟨a, b | aabbbabba=1⟩φ(a) = b, φ(b) = a
112967⟨a, b | aaabbabaaab=1⟩φ(a) = aad, φ(b) = aaab
113024⟨a, b | aabaaabbaba=1⟩φ(a) = aad, φ(b) = aaba
113116⟨a, b | aabbabaaaba=1⟩φ(a) = aad, φ(b) = aaba
113263⟨a, b | ababbbabbba=1⟩φ(a) = abaa, φ(b) = aad

Anti-isomorphic instances

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

7 total

Σ#PresentationMapping
9685⟨a, b | aabbabbba=1⟩φ(a) = b, φ(b) = a
9687⟨a, b | aabbbaaba=1⟩φ(a) = a, φ(b) = b
9702⟨a, b | abaaabbba=1⟩φ(a) = a, φ(b) = b
112941⟨a, b | aaababbaaab=1⟩φ(a) = aad, φ(b) = aaab
113022⟨a, b | aabaaababba=1⟩φ(a) = aad, φ(b) = abaa
113075⟨a, b | aababbaaaba=1⟩φ(a) = aad, φ(b) = abaa
113273⟨a, b | abbaaabaaab=1⟩φ(a) = aad, φ(b) = aaba