#1350 ⟨a, b | aaabaabbba=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. cd ⇒ 1 [20]
2. dc ⇒ 1 [11]
3. bc ⇒ cb [5]
4. bd ⇒ db [24]
5. b3 ⇒ c [2]
6. ba2ca ⇒ aba2c [12]
7. b2aba2 ⇒ ca2cad [27]
8. ca4 ⇒ (a2b)2b [29]
9. da2ba2 ⇒ a4db [31]
10. cba4 ⇒ (ba2)2b2 [30]
11. d(ba2)2 ⇒ ba4db [25]
12. b2a4 ⇒ a2ca2db2 [32]
13. b(ba2)2 ⇒ (ca2)2d [34]
14. da3ba2 ⇒ a4bad [7]
15. dba3ba2 ⇒ ba4bad [35]
16. b2a3ba2 ⇒ ca2ca3d [36]
17. a4ba2 ⇒ d [3]
# ab:aaabaabbba=1 cdb/a bbb=c,aaaabaa=d magic:1
cd=1
dc=1
bc=cb
bd=db
bbb=c
baaca=abaac
bbabaa=caacad
caaaa=aabaabb
daabaa=aaaadb
cbaaaa=baabaabb
dbaabaa=baaaadb
bbaaaa=aacaadbb
bbaabaa=caacaad
daaabaa=aaaabad
dbaaabaa=baaaabad
bbaaabaa=caacaaad
aaaabaa=d

Other submonoids of same group

1 unique, 1 total

Σ#PresentationDescriptionRelated
101999⟨a, b | aabbabba=bb⟩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
101412⟨a, b | aabaabbbaa=1⟩φ(a) = a, φ(b) = b
101457⟨a, b | aabbbaaaab=1⟩φ(a) = a, φ(b) = b
101469⟨a, b | aabbbbabba=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
101379⟨a, b | aaabbbaaba=1⟩φ(a) = a, φ(b) = b
101456⟨a, b | aabbabbbba=1⟩φ(a) = b, φ(b) = a
101482⟨a, b | abaaaabbba=1⟩φ(a) = a, φ(b) = b