#2087 ⟨a, b | abbbaaab=ba⟩

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Contents

  1. Properties
  2. Rewriting system

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. (dc)3b ⇒ c [5]
2. dc(dcd)2cbd ⇒ cb [10]
3. (dc)2(d(dc)2)2bc ⇒ c2(dc)2b [13]
4. (d(dc)2)2(d2c)2dcbd2 ⇒ cdb [20]
5. cb2 ⇒ (dc)2bd [9]
6. cbc(dc)2b ⇒ dc(dcd)2cbc [11]
7. cdbc(dc)2b ⇒ (d(dc)2)2(d2c)2dcbdc [22]
8. c2dcbdb ⇒ dc(dcd)2c((d2c)2dc)2bd2 [29]
9. c(dc)2bdb ⇒ (dc)2d2c(dcd)3cbd2 [18]
10. d(dc)2bdb ⇒ bd [16]
11. c2((dc)2b)2 ⇒ dc((dcd)2cd)2(dc)2bc [15]
12. dc(dcd)2(cb)2 ⇒ cbc(dcd)2cbd [12]
13. dc(dcd)2cbcdb ⇒ cb(dc)2d2c(dcd)3cbd2 [21]
14. dc(dcd)2cbc2(dc)2b ⇒ cbcdc(d(dc)2)2bc [14]
15. (d(dc)2)2(d2c)2dcbcdb ⇒ cdbcdcd2c(dcd)3cbd2 [27]
16. (d(dc)2)2(d2c)2(dcb)2 ⇒ cdbc(dcd)2cbd [23]
17. (d(dc)2)2(d2c)2dcbdcdb ⇒ cdb(dc)2d2c(dcd)3cbd2 [28]
18. (d(dc)2)2(d2c)2dcbdc2(dc)2b ⇒ cdbcdc(d(dc)2)2bc [24]
19. cbcdcbdb ⇒ (dc)2((d2c)2dc)2bd2 [19]
20. cb(dc)2bdb ⇒ dc(dcd)3cbd2 [17]
21. cdbcdcbdb ⇒ (d(dc)2)2(d2c)3dcbd2 [25]
22. cdb(dc)2bdb ⇒ d2c(dcd2c)2bd2 [26]
23. c(cd)2(cbd)2b ⇒ dc(dcd)2c((d2c)2dc)3bd2 [30]
24. ab2 ⇒ d [3]
25. ca ⇒ dc2 [8]
26. da ⇒ abdcb [6]
27. ba ⇒ dcb [4]
# ab:abbbaaab=ba cd/b/a baaa=c,abb=d morph:4/3,3/0
dcdcdcb=c
dcdcddcdcbd=cb
dcdcddcdcddcdcbc=ccdcdcb
ddcdcddcdcddcddcdcbdd=cdb
cbb=dcdcbd
cbcdcdcb=dcdcddcdcbc
cdbcdcdcb=ddcdcddcdcddcddcdcbdc
ccdcbdb=dcdcddcdcddcddcdcddcddcdcbdd
cdcdcbdb=dcdcddcdcddcddcdcbdd
ddcdcbdb=bd
ccdcdcbdcdcb=dcdcddcdcddcddcdcddcdcbc
dcdcddcdcbcb=cbcdcddcdcbd
dcdcddcdcbcdb=cbdcdcddcdcddcddcdcbdd
dcdcddcdcbccdcdcb=cbcdcddcdcddcdcbc
ddcdcddcdcddcddcdcbcdb=cdbcdcddcdcddcddcdcbdd
ddcdcddcdcddcddcdcbdcb=cdbcdcddcdcbd
ddcdcddcdcddcddcdcbdcdb=cdbdcdcddcdcddcddcdcbdd
ddcdcddcdcddcddcdcbdccdcdcb=cdbcdcddcdcddcdcbc
cbcdcbdb=dcdcddcddcdcddcddcdcbdd
cbdcdcbdb=dcdcddcddcdcbdd
cdbcdcbdb=ddcdcddcdcddcddcddcdcbdd
cdbdcdcbdb=ddcdcddcdcddcbdd
ccdcdcbdcbdb=dcdcddcdcddcddcdcddcddcdcddcddcdcbdd
abb=d
ca=dcc
da=abdcb
ba=dcb