YES

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

Proof:
 DP Processor:
  DPs:
   w#(r(x)) -> w#(x)
   b#(r(x)) -> b#(x)
   b#(w(x)) -> b#(x)
   b#(w(x)) -> w#(b(x))
  TRS:
   w(r(x)) -> r(w(x))
   b(r(x)) -> r(b(x))
   b(w(x)) -> w(b(x))
  CDG Processor:
   DPs:
    w#(r(x)) -> w#(x)
    b#(r(x)) -> b#(x)
    b#(w(x)) -> b#(x)
    b#(w(x)) -> w#(b(x))
   TRS:
    w(r(x)) -> r(w(x))
    b(r(x)) -> r(b(x))
    b(w(x)) -> w(b(x))
   graph:
    b#(w(x)) -> b#(x) -> b#(r(x)) -> b#(x)
    b#(w(x)) -> b#(x) -> b#(w(x)) -> b#(x)
    b#(w(x)) -> b#(x) -> b#(w(x)) -> w#(b(x))
    b#(w(x)) -> w#(b(x)) -> w#(r(x)) -> w#(x)
    b#(r(x)) -> b#(x) -> b#(r(x)) -> b#(x)
    b#(r(x)) -> b#(x) -> b#(w(x)) -> b#(x)
    b#(r(x)) -> b#(x) -> b#(w(x)) -> w#(b(x))
    w#(r(x)) -> w#(x) -> w#(r(x)) -> w#(x)
   Restore Modifier:
    DPs:
     w#(r(x)) -> w#(x)
     b#(r(x)) -> b#(x)
     b#(w(x)) -> b#(x)
     b#(w(x)) -> w#(b(x))
    TRS:
     w(r(x)) -> r(w(x))
     b(r(x)) -> r(b(x))
     b(w(x)) -> w(b(x))
    SCC Processor:
     #sccs: 2
     #rules: 3
     #arcs: 8/16
     DPs:
      b#(w(x)) -> b#(x)
      b#(r(x)) -> b#(x)
     TRS:
      w(r(x)) -> r(w(x))
      b(r(x)) -> r(b(x))
      b(w(x)) -> w(b(x))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = x0 + 1,
       
       [b](x0) = x0 + 1,
       
       [w](x0) = x0,
       
       [r](x0) = x0 + 1
      orientation:
       b#(w(x)) = x + 1 >= x + 1 = b#(x)
       
       b#(r(x)) = x + 2 >= x + 1 = b#(x)
       
       w(r(x)) = x + 1 >= x + 1 = r(w(x))
       
       b(r(x)) = x + 2 >= x + 2 = r(b(x))
       
       b(w(x)) = x + 1 >= x + 1 = w(b(x))
      problem:
       DPs:
        b#(w(x)) -> b#(x)
       TRS:
        w(r(x)) -> r(w(x))
        b(r(x)) -> r(b(x))
        b(w(x)) -> w(b(x))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [b#](x0) = x0,
        
        [b](x0) = x0 + 1,
        
        [w](x0) = x0 + 1,
        
        [r](x0) = 0
       orientation:
        b#(w(x)) = x + 1 >= x = b#(x)
        
        w(r(x)) = 1 >= 0 = r(w(x))
        
        b(r(x)) = 1 >= 0 = r(b(x))
        
        b(w(x)) = x + 2 >= x + 2 = w(b(x))
       problem:
        DPs:
         
        TRS:
         w(r(x)) -> r(w(x))
         b(r(x)) -> r(b(x))
         b(w(x)) -> w(b(x))
       Qed
     
     DPs:
      w#(r(x)) -> w#(x)
     TRS:
      w(r(x)) -> r(w(x))
      b(r(x)) -> r(b(x))
      b(w(x)) -> w(b(x))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [w#](x0) = x0 + 1,
       
       [b](x0) = x0 + 1,
       
       [w](x0) = x0,
       
       [r](x0) = x0 + 1
      orientation:
       w#(r(x)) = x + 2 >= x + 1 = w#(x)
       
       w(r(x)) = x + 1 >= x + 1 = r(w(x))
       
       b(r(x)) = x + 2 >= x + 2 = r(b(x))
       
       b(w(x)) = x + 1 >= x + 1 = w(b(x))
      problem:
       DPs:
        
       TRS:
        w(r(x)) -> r(w(x))
        b(r(x)) -> r(b(x))
        b(w(x)) -> w(b(x))
      Qed