YES

1 decompositions
 #1 -----------
   1: b(w(x1)) -> w(w(w(b(x1))))
   2: w(b(x2)) -> b(x2)
   3: b(b(x3)) -> w(w(w(w(x3))))
   4: w(w(x4)) -> w(x4)

@Knuth and Bendix' criterion
--- R
   1: b(w(x1)) -> w(w(w(b(x1))))
   2: w(b(x2)) -> b(x2)
   3: b(b(x3)) -> w(w(w(w(x3))))
   4: w(w(x4)) -> w(x4)

--- S
   1: b(w(x1)) -> w(w(w(b(x1))))
   2: w(b(x2)) -> b(x2)
   3: b(b(x3)) -> w(w(w(w(x3))))
   4: w(w(x4)) -> w(x4)