YES

1 decompositions
 #1 -----------
   1: W(B(x1)) -> W(x1)
   2: B(I(x1)) -> J(x1)
   3: W(I(x1)) -> W(J(x1))

@Jouannaud and Kirchner's criterion
--- R
   1: W(B(x1)) -> W(x1)
   2: B(I(x1)) -> J(x1)
   3: W(I(x1)) -> W(J(x1))

--- S
   1: W(B(x1)) -> W(x1)
   2: B(I(x1)) -> J(x1)
   3: W(I(x1)) -> W(J(x1))