YES

1 decompositions
 #0 -----------
   1: b(w(x)) -> w(w(w(b(x))))
   2: w(b(x)) -> b(x)
   3: b(b(x)) -> w(w(w(w(x))))
   4: w(w(x)) -> w(x)

@Jouannaud and Kirchner's criterion
--- R
   1: b(w(x)) -> w(w(w(b(x))))
   2: w(b(x)) -> b(x)
   3: b(b(x)) -> w(w(w(w(x))))
   4: w(w(x)) -> w(x)

--- S
   1: b(w(x)) -> w(w(w(b(x))))
   2: w(b(x)) -> b(x)
   3: b(b(x)) -> w(w(w(w(x))))
   4: w(w(x)) -> w(x)