#1377 ⟨a, b | aaabbabbba=1⟩

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Quick links

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances
  5. 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 [13]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [12]
5. a4 ⇒ c [2]
6. b3c ⇒ a3b2ab [17]
7. b2abd ⇒ adb3 [14]
8. bcb2a ⇒ cb2ab [24]
9. b3ac ⇒ a3b(ba)2 [19]
10. b(ba)2d ⇒ adb3a [15]
11. b3a2c ⇒ a3b2aba2 [26]
12. b2aba2d ⇒ adb3a2 [20]
13. b3a3 ⇒ a3dbcb2 [29]
14. b2aba3 ⇒ dbcb2c [25]
15. b2ab2d ⇒ dbab3 [10]
16. (b2a)2d ⇒ dbab3a [21]
17. (b2a)2ad ⇒ dbab3a2 [30]
18. b2ab2a3 ⇒ d(b2c)2 [27]
19. b2ab3 ⇒ d [3]
# ab:aaabbabbba=1 reversed:cda/b aaaa=c,bbabbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
bbbc=aaabbab
bbabd=adbbb
bcbba=cbbab
bbbac=aaabbaba
bbabad=adbbba
bbbaac=aaabbabaa
bbabaad=adbbbaa
bbbaaa=aaadbcbb
bbabaaa=dbcbbc
bbabbd=dbabbb
bbabbad=dbabbba
bbabbaad=dbabbbaa
bbabbaaa=dbbcbbc
bbabbb=d

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
114798⟨a, b | abaababa=bbb⟩Infinite cancellative non-commutative monoid

Isomorphic instances

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

3 total

Σ#PresentationMapping
101454⟨a, b | aabbabbbaa=1⟩φ(a) = a, φ(b) = b
101467⟨a, b | aabbbbaaba=1⟩φ(a) = b, φ(b) = a
101490⟨a, b | abaaabbbba=1⟩φ(a) = b, 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
101383⟨a, b | aaabbbabba=1⟩φ(a) = a, φ(b) = b
101414⟨a, b | aabaabbbba=1⟩φ(a) = b, φ(b) = a
101466⟨a, b | aabbbbaaab=1⟩φ(a) = b, φ(b) = a