#2926 ⟨a, b | aaabaabbbba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Isomorphic instances
  4. 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. cd ⇒ 1 [20]
2. dc ⇒ 1 [11]
3. bc ⇒ cb [5]
4. bd ⇒ db [24]
5. b4 ⇒ c [2]
6. ba2ca ⇒ aba2c [12]
7. b3aba2 ⇒ ca2cad [29]
8. ca4 ⇒ a2ba2b3 [27]
9. da2ba2 ⇒ a4db [32]
10. cba4 ⇒ (ba2)2b3 [30]
11. d(ba2)2 ⇒ ba4db [25]
12. cb2a4 ⇒ b(ba2)2b3 [35]
13. db(ba2)2 ⇒ b2a4db [31]
14. b3a4 ⇒ a2ca2db3 [33]
15. b2(ba2)2 ⇒ (ca2)2d [37]
16. da3ba2 ⇒ a4bad [7]
17. dba3ba2 ⇒ ba4bad [34]
18. db2a3ba2 ⇒ b2a4bad [38]
19. b3a3ba2 ⇒ ca2ca3d [39]
20. a4ba2 ⇒ d [3]
# ab:aaabaabbbba=1 cdb/a bbbb=c,aaaabaa=d magic:1
cd=1
dc=1
bc=cb
bd=db
bbbb=c
baaca=abaac
bbbabaa=caacad
caaaa=aabaabbb
daabaa=aaaadb
cbaaaa=baabaabbb
dbaabaa=baaaadb
cbbaaaa=bbaabaabbb
dbbaabaa=bbaaaadb
bbbaaaa=aacaadbbb
bbbaabaa=caacaad
daaabaa=aaaabad
dbaaabaa=baaaabad
dbbaaabaa=bbaaaabad
bbbaaabaa=caacaaad
aaaabaa=d

Isomorphic instances

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

3 total

Σ#PresentationMapping
112997⟨a, b | aaabbbbabba=1⟩φ(a) = b, φ(b) = a
113049⟨a, b | aabaabbbbaa=1⟩φ(a) = a, φ(b) = b
113152⟨a, b | aabbbbaaaab=1⟩φ(a) = a, φ(b) = b

Anti-isomorphic instances

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

4 total

Σ#PresentationMapping
112979⟨a, b | aaabbabbbba=1⟩φ(a) = b, φ(b) = a
112993⟨a, b | aaabbbbaaba=1⟩φ(a) = a, φ(b) = b
113131⟨a, b | aabbabbbbaa=1⟩φ(a) = b, φ(b) = a
113184⟨a, b | abaaaabbbba=1⟩φ(a) = a, φ(b) = b