YES

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

Proof:
 Church Rosser Transformation Processor (critical pair closing system, Thm 2.4):
  W(W(x22)) -> W(x22)
  B(I(x23)) -> W(x23)
  critical peaks: joinable
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [W](x0) = x0,
    
    [B](x0) = x0 + 1,
    
    [I](x0) = x0 + 6
   orientation:
    W(W(x22)) = x22 >= x22 = W(x22)
    
    B(I(x23)) = x23 + 7 >= x23 = W(x23)
   problem:
    W(W(x22)) -> W(x22)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [W](x0) = 2x0 + 5
    orientation:
     W(W(x22)) = 4x22 + 15 >= 2x22 + 5 = W(x22)
    problem:
     
    Qed