YES

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

@Jouannaud and Kirchner's criterion
--- R
   1: b(w(x1)) -> w(w(w(b(x1))))
   2: w(b(x1)) -> b(x1)
   3: b(b(x1)) -> w(w(w(w(x1))))
   4: w(w(x1)) -> w(x1)

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