YES

Problem:
 W(B(x)) -> W(x)
 B(I(x)) -> J(x)
 W(I(x)) -> W(J(x))

Proof:
 Church Rosser Transformation Processor (kb):
  W(B(x)) -> W(x)
  B(I(x)) -> J(x)
  W(I(x)) -> W(J(x))
  critical peaks: joinable
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [W](x0) = 4x0 + 3,
     
     [J](x0) = x0,
     
     [B](x0) = x0,
     
     [I](x0) = 2x0 + 4
    orientation:
     W(B(x)) = 4x + 3 >= 4x + 3 = W(x)
     
     B(I(x)) = 2x + 4 >= x = J(x)
     
     W(I(x)) = 8x + 19 >= 4x + 3 = W(J(x))
    problem:
     W(B(x)) -> W(x)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [W](x0) = x0,
      
      [B](x0) = x0 + 3
     orientation:
      W(B(x)) = x + 3 >= x = W(x)
     problem:
      
     Qed