YES

Problem:
 a(c(d(x))) -> c(x)
 u(b(d(d(x)))) -> b(x)
 v(a(a(x))) -> u(v(x))
 v(a(c(x))) -> u(b(d(x)))
 v(c(x)) -> b(x)
 w(a(a(x))) -> u(w(x))
 w(a(c(x))) -> u(b(d(x)))
 w(c(x)) -> b(x)

Proof:
 DP Processor:
  DPs:
   v#(a(a(x))) -> v#(x)
   v#(a(a(x))) -> u#(v(x))
   v#(a(c(x))) -> u#(b(d(x)))
   w#(a(a(x))) -> w#(x)
   w#(a(a(x))) -> u#(w(x))
   w#(a(c(x))) -> u#(b(d(x)))
  TRS:
   a(c(d(x))) -> c(x)
   u(b(d(d(x)))) -> b(x)
   v(a(a(x))) -> u(v(x))
   v(a(c(x))) -> u(b(d(x)))
   v(c(x)) -> b(x)
   w(a(a(x))) -> u(w(x))
   w(a(c(x))) -> u(b(d(x)))
   w(c(x)) -> b(x)
  Usable Rule Processor:
   DPs:
    v#(a(a(x))) -> v#(x)
    v#(a(a(x))) -> u#(v(x))
    v#(a(c(x))) -> u#(b(d(x)))
    w#(a(a(x))) -> w#(x)
    w#(a(a(x))) -> u#(w(x))
    w#(a(c(x))) -> u#(b(d(x)))
   TRS:
    v(a(a(x))) -> u(v(x))
    v(a(c(x))) -> u(b(d(x)))
    v(c(x)) -> b(x)
    u(b(d(d(x)))) -> b(x)
    w(a(a(x))) -> u(w(x))
    w(a(c(x))) -> u(b(d(x)))
    w(c(x)) -> b(x)
   EDG Processor:
    DPs:
     v#(a(a(x))) -> v#(x)
     v#(a(a(x))) -> u#(v(x))
     v#(a(c(x))) -> u#(b(d(x)))
     w#(a(a(x))) -> w#(x)
     w#(a(a(x))) -> u#(w(x))
     w#(a(c(x))) -> u#(b(d(x)))
    TRS:
     v(a(a(x))) -> u(v(x))
     v(a(c(x))) -> u(b(d(x)))
     v(c(x)) -> b(x)
     u(b(d(d(x)))) -> b(x)
     w(a(a(x))) -> u(w(x))
     w(a(c(x))) -> u(b(d(x)))
     w(c(x)) -> b(x)
    graph:
     w#(a(a(x))) -> w#(x) -> w#(a(a(x))) -> w#(x)
     w#(a(a(x))) -> w#(x) -> w#(a(a(x))) -> u#(w(x))
     w#(a(a(x))) -> w#(x) -> w#(a(c(x))) -> u#(b(d(x)))
     v#(a(a(x))) -> v#(x) -> v#(a(a(x))) -> v#(x)
     v#(a(a(x))) -> v#(x) -> v#(a(a(x))) -> u#(v(x))
     v#(a(a(x))) -> v#(x) -> v#(a(c(x))) -> u#(b(d(x)))
    Restore Modifier:
     DPs:
      v#(a(a(x))) -> v#(x)
      v#(a(a(x))) -> u#(v(x))
      v#(a(c(x))) -> u#(b(d(x)))
      w#(a(a(x))) -> w#(x)
      w#(a(a(x))) -> u#(w(x))
      w#(a(c(x))) -> u#(b(d(x)))
     TRS:
      a(c(d(x))) -> c(x)
      u(b(d(d(x)))) -> b(x)
      v(a(a(x))) -> u(v(x))
      v(a(c(x))) -> u(b(d(x)))
      v(c(x)) -> b(x)
      w(a(a(x))) -> u(w(x))
      w(a(c(x))) -> u(b(d(x)))
      w(c(x)) -> b(x)
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 6/36
      DPs:
       v#(a(a(x))) -> v#(x)
      TRS:
       a(c(d(x))) -> c(x)
       u(b(d(d(x)))) -> b(x)
       v(a(a(x))) -> u(v(x))
       v(a(c(x))) -> u(b(d(x)))
       v(c(x)) -> b(x)
       w(a(a(x))) -> u(w(x))
       w(a(c(x))) -> u(b(d(x)))
       w(c(x)) -> b(x)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [v#](x0) = x0,
        
        [w](x0) = 0,
        
        [v](x0) = x0,
        
        [u](x0) = 0,
        
        [b](x0) = 0,
        
        [a](x0) = x0 + 1,
        
        [c](x0) = 0,
        
        [d](x0) = 0
       orientation:
        v#(a(a(x))) = x + 2 >= x = v#(x)
        
        a(c(d(x))) = 1 >= 0 = c(x)
        
        u(b(d(d(x)))) = 0 >= 0 = b(x)
        
        v(a(a(x))) = x + 2 >= 0 = u(v(x))
        
        v(a(c(x))) = 1 >= 0 = u(b(d(x)))
        
        v(c(x)) = 0 >= 0 = b(x)
        
        w(a(a(x))) = 0 >= 0 = u(w(x))
        
        w(a(c(x))) = 0 >= 0 = u(b(d(x)))
        
        w(c(x)) = 0 >= 0 = b(x)
       problem:
        DPs:
         
        TRS:
         a(c(d(x))) -> c(x)
         u(b(d(d(x)))) -> b(x)
         v(a(a(x))) -> u(v(x))
         v(a(c(x))) -> u(b(d(x)))
         v(c(x)) -> b(x)
         w(a(a(x))) -> u(w(x))
         w(a(c(x))) -> u(b(d(x)))
         w(c(x)) -> b(x)
       Qed
      
      DPs:
       w#(a(a(x))) -> w#(x)
      TRS:
       a(c(d(x))) -> c(x)
       u(b(d(d(x)))) -> b(x)
       v(a(a(x))) -> u(v(x))
       v(a(c(x))) -> u(b(d(x)))
       v(c(x)) -> b(x)
       w(a(a(x))) -> u(w(x))
       w(a(c(x))) -> u(b(d(x)))
       w(c(x)) -> b(x)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [w#](x0) = x0,
        
        [w](x0) = 0,
        
        [v](x0) = x0,
        
        [u](x0) = 0,
        
        [b](x0) = 0,
        
        [a](x0) = x0 + 1,
        
        [c](x0) = 0,
        
        [d](x0) = 0
       orientation:
        w#(a(a(x))) = x + 2 >= x = w#(x)
        
        a(c(d(x))) = 1 >= 0 = c(x)
        
        u(b(d(d(x)))) = 0 >= 0 = b(x)
        
        v(a(a(x))) = x + 2 >= 0 = u(v(x))
        
        v(a(c(x))) = 1 >= 0 = u(b(d(x)))
        
        v(c(x)) = 0 >= 0 = b(x)
        
        w(a(a(x))) = 0 >= 0 = u(w(x))
        
        w(a(c(x))) = 0 >= 0 = u(b(d(x)))
        
        w(c(x)) = 0 >= 0 = b(x)
       problem:
        DPs:
         
        TRS:
         a(c(d(x))) -> c(x)
         u(b(d(d(x)))) -> b(x)
         v(a(a(x))) -> u(v(x))
         v(a(c(x))) -> u(b(d(x)))
         v(c(x)) -> b(x)
         w(a(a(x))) -> u(w(x))
         w(a(c(x))) -> u(b(d(x)))
         w(c(x)) -> b(x)
       Qed