#21739 ⟨a, b | aaa=1, abbabba=b⟩

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  1. Properties
  2. Rewriting system

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. db ⇒ bd [38]
2. b3d ⇒ b [34]
3. b2d2 ⇒ d [42]
4. cb2d ⇒ c [44]
5. dc ⇒ bcbd2 [43]
6. b3c ⇒ cb3 [14]
7. (bc)2 ⇒ c2b14 [67]
8. b2c2 ⇒ (cb)2d6 [62]
9. c3 ⇒ b2d [6]
10. bab2d ⇒ ba [35]
11. da ⇒ babd2 [51]
12. b3a ⇒ ab3 [11]
13. ca ⇒ bacb5 [20]
14. cba ⇒ b2ab2cbd2 [46]
15. cb2a ⇒ abcbd3 [57]
16. a2b ⇒ bac2b3 [22]
17. a2d ⇒ bac2 [5]
18. a2c ⇒ bac2b2c [24]
19. aba ⇒ bcbd2 [47]
20. ab2a ⇒ b2ac2 [29]
21. ba2 ⇒ b2ac2b2 [45]
22. a3 ⇒ 1 [1]
# ab:aaa=1,abbabba=b bd/c/a bbaba=c,abacc=d morph:5/0,5/0
db=bd
bbbd=b
bbdd=d
cbbd=c
dc=bcbdd
bbbc=cbbb
bcbc=ccbbbbbbbbbbbbbb
bbcc=cbcbdddddd
ccc=bbd
babbd=ba
da=babdd
bbba=abbb
ca=bacbbbbb
cba=bbabbcbdd
cbba=abcbddd
aab=baccbbb
aad=bacc
aac=baccbbc
aba=bcbdd
abba=bbacc
baa=bbaccbb
aaa=1