#4353 ⟨a, b | abbbaaaab=ba⟩

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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. (dc)4b ⇒ c [5]
2. d(cd)3(dc)3bd ⇒ cb [10]
3. (dc)3(d(dc)3)2bc ⇒ c2(dc)3b [13]
4. d(dc)3d2c(d(cd)2)3cbd2 ⇒ cdb [20]
5. cb2 ⇒ (dc)3bd [9]
6. cbc(dc)3b ⇒ d(cd)3(dc)3bc [11]
7. cdbc(dc)3b ⇒ d(dc)3d2c(d(cd)2)3cbdc [22]
8. c2(dc)2bdb ⇒ d(cd)3(dc)3(d(d(cd)2)2c)2bd2 [29]
9. c(dc)3bdb ⇒ (dc)3d2c(d(cd)2)3cbd2 [18]
10. d(dc)3bdb ⇒ bd [16]
11. c2((dc)3b)2 ⇒ dc((d(cd)2)2cd)2(dc)3bc [15]
12. d(cd)3(dc)3bcb ⇒ cb(cd)3(dc)3bd [12]
13. d(cd)3(dc)3bcdb ⇒ cb(dc)3d2c(d(cd)2)3cbd2 [21]
14. d(cd)3(dc)3bc2(dc)3b ⇒ cbc(dc)2(d(dc)3)2bc [14]
15. d(dc)3d2c(d(cd)2)3cbcdb ⇒ cdb(cd)3dc(d(cd)2)3cbd2 [27]
16. (d(dc)3)2(d(dc)2)2(dcb)2 ⇒ cdb(cd)3(dc)3bd [23]
17. d(dc)3d2c(d(cd)2)3cbdcdb ⇒ cdb(dc)3d2c(d(cd)2)3cbd2 [28]
18. d(dc)3d2c(d(cd)2)3cbdc2(dc)3b ⇒ cdbc(dc)2(d(dc)3)2bc [24]
19. cbc(dc)2bdb ⇒ (dc)3(d(d(cd)2)2c)2bd2 [19]
20. cb(dc)3bdb ⇒ dc(d(cd)2)3cbd2 [17]
21. cdbc(dc)2bdb ⇒ d(dc)3d2c(d(cd)2)4cbd2 [25]
22. cdb(dc)3bdb ⇒ d(d(cd)3)2(dc)2bd2 [26]
23. c2dc((dc)2b)2db ⇒ d(cd)3(dc)3(d(d(cd)2)2c)3bd2 [30]
24. ab2 ⇒ d [3]
25. ca ⇒ dc2 [8]
26. da ⇒ abdcb [6]
27. ba ⇒ dcb [4]
# ab:abbbaaaab=ba cd/b/a baaaa=c,abb=d morph:5/2,3/0
dcdcdcdcb=c
dcdcdcddcdcdcbd=cb
dcdcdcddcdcdcddcdcdcbc=ccdcdcdcb
ddcdcdcddcdcdcddcdcddcdcdcbdd=cdb
cbb=dcdcdcbd
cbcdcdcdcb=dcdcdcddcdcdcbc
cdbcdcdcdcb=ddcdcdcddcdcdcddcdcddcdcdcbdc
ccdcdcbdb=dcdcdcddcdcdcddcdcddcdcdcddcdcddcdcdcbdd
cdcdcdcbdb=dcdcdcddcdcdcddcdcddcdcdcbdd
ddcdcdcbdb=bd
ccdcdcdcbdcdcdcb=dcdcdcddcdcdcddcdcddcdcdcddcdcdcbc
dcdcdcddcdcdcbcb=cbcdcdcddcdcdcbd
dcdcdcddcdcdcbcdb=cbdcdcdcddcdcdcddcdcddcdcdcbdd
dcdcdcddcdcdcbccdcdcdcb=cbcdcdcddcdcdcddcdcdcbc
ddcdcdcddcdcdcddcdcddcdcdcbcdb=cdbcdcdcddcdcdcddcdcddcdcdcbdd
ddcdcdcddcdcdcddcdcddcdcdcbdcb=cdbcdcdcddcdcdcbd
ddcdcdcddcdcdcddcdcddcdcdcbdcdb=cdbdcdcdcddcdcdcddcdcddcdcdcbdd
ddcdcdcddcdcdcddcdcddcdcdcbdccdcdcdcb=cdbcdcdcddcdcdcddcdcdcbc
cbcdcdcbdb=dcdcdcddcdcddcdcdcddcdcddcdcdcbdd
cbdcdcdcbdb=dcdcdcddcdcddcdcdcbdd
cdbcdcdcbdb=ddcdcdcddcdcdcddcdcddcdcddcdcdcbdd
cdbdcdcdcbdb=ddcdcdcddcdcdcddcdcbdd
ccdcdcdcbdcdcbdb=dcdcdcddcdcdcddcdcddcdcdcddcdcddcdcdcddcdcddcdcdcbdd
abb=d
ca=dcc
da=abdcb
ba=dcb