YES

Problem:
 b(w(x)) -> w(w(w(b(x))))
 w(b(x)) -> b(x)
 b(b(x)) -> w(w(w(w(x))))
 w(w(x)) -> w(x)

Proof:
 Church Rosser Transformation Processor (kb):
  b(w(x)) -> w(w(w(b(x))))
  w(b(x)) -> b(x)
  b(b(x)) -> w(w(w(w(x))))
  w(w(x)) -> w(x)
  critical peaks: joinable
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [b](x0) = x0 + 4,
     
     [w](x0) = x0
    orientation:
     b(w(x)) = x + 4 >= x + 4 = w(w(w(b(x))))
     
     w(b(x)) = x + 4 >= x + 4 = b(x)
     
     b(b(x)) = x + 8 >= x = w(w(w(w(x))))
     
     w(w(x)) = x >= x = w(x)
    problem:
     b(w(x)) -> w(w(w(b(x))))
     w(b(x)) -> b(x)
     w(w(x)) -> w(x)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [b](x0) = 4x0,
      
      [w](x0) = x0 + 2
     orientation:
      b(w(x)) = 4x + 8 >= 4x + 6 = w(w(w(b(x))))
      
      w(b(x)) = 4x + 2 >= 4x = b(x)
      
      w(w(x)) = x + 4 >= x + 2 = w(x)
     problem:
      
     Qed