YES

Problem:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(1(1(x1)))) -> 0(0(0(1(x1))))

Proof:
 DP Processor:
  DPs:
   0#(0(0(0(x1)))) -> 1#(x1)
   0#(0(0(0(x1)))) -> 1#(1(x1))
   0#(0(0(0(x1)))) -> 1#(1(1(x1)))
   0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
   1#(0(1(1(x1)))) -> 0#(1(x1))
   1#(0(1(1(x1)))) -> 0#(0(1(x1)))
   1#(0(1(1(x1)))) -> 0#(0(0(1(x1))))
  TRS:
   0(0(0(0(x1)))) -> 0(1(1(1(x1))))
   1(0(1(1(x1)))) -> 0(0(0(1(x1))))
  TDG Processor:
   DPs:
    0#(0(0(0(x1)))) -> 1#(x1)
    0#(0(0(0(x1)))) -> 1#(1(x1))
    0#(0(0(0(x1)))) -> 1#(1(1(x1)))
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
    1#(0(1(1(x1)))) -> 0#(1(x1))
    1#(0(1(1(x1)))) -> 0#(0(1(x1)))
    1#(0(1(1(x1)))) -> 0#(0(0(1(x1))))
   TRS:
    0(0(0(0(x1)))) -> 0(1(1(1(x1))))
    1(0(1(1(x1)))) -> 0(0(0(1(x1))))
   graph:
    1#(0(1(1(x1)))) -> 0#(1(x1)) -> 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
    1#(0(1(1(x1)))) -> 0#(1(x1)) -> 0#(0(0(0(x1)))) -> 1#(1(1(x1)))
    1#(0(1(1(x1)))) -> 0#(1(x1)) -> 0#(0(0(0(x1)))) -> 1#(1(x1))
    1#(0(1(1(x1)))) -> 0#(1(x1)) -> 0#(0(0(0(x1)))) -> 1#(x1)
    1#(0(1(1(x1)))) -> 0#(0(1(x1))) ->
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
    1#(0(1(1(x1)))) -> 0#(0(1(x1))) ->
    0#(0(0(0(x1)))) -> 1#(1(1(x1)))
    1#(0(1(1(x1)))) -> 0#(0(1(x1))) -> 0#(0(0(0(x1)))) -> 1#(1(x1))
    1#(0(1(1(x1)))) -> 0#(0(1(x1))) -> 0#(0(0(0(x1)))) -> 1#(x1)
    1#(0(1(1(x1)))) -> 0#(0(0(1(x1)))) ->
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
    1#(0(1(1(x1)))) -> 0#(0(0(1(x1)))) ->
    0#(0(0(0(x1)))) -> 1#(1(1(x1)))
    1#(0(1(1(x1)))) -> 0#(0(0(1(x1)))) ->
    0#(0(0(0(x1)))) -> 1#(1(x1))
    1#(0(1(1(x1)))) -> 0#(0(0(1(x1)))) -> 0#(0(0(0(x1)))) -> 1#(x1)
    0#(0(0(0(x1)))) -> 1#(1(1(x1))) ->
    1#(0(1(1(x1)))) -> 0#(0(0(1(x1))))
    0#(0(0(0(x1)))) -> 1#(1(1(x1))) ->
    1#(0(1(1(x1)))) -> 0#(0(1(x1)))
    0#(0(0(0(x1)))) -> 1#(1(1(x1))) -> 1#(0(1(1(x1)))) -> 0#(1(x1))
    0#(0(0(0(x1)))) -> 1#(1(x1)) -> 1#(0(1(1(x1)))) -> 0#(0(0(1(x1))))
    0#(0(0(0(x1)))) -> 1#(1(x1)) -> 1#(0(1(1(x1)))) -> 0#(0(1(x1)))
    0#(0(0(0(x1)))) -> 1#(1(x1)) -> 1#(0(1(1(x1)))) -> 0#(1(x1))
    0#(0(0(0(x1)))) -> 1#(x1) -> 1#(0(1(1(x1)))) -> 0#(0(0(1(x1))))
    0#(0(0(0(x1)))) -> 1#(x1) -> 1#(0(1(1(x1)))) -> 0#(0(1(x1)))
    0#(0(0(0(x1)))) -> 1#(x1) -> 1#(0(1(1(x1)))) -> 0#(1(x1))
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1)))) ->
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1)))) ->
    0#(0(0(0(x1)))) -> 1#(1(1(x1)))
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1)))) ->
    0#(0(0(0(x1)))) -> 1#(1(x1))
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1)))) -> 0#(0(0(0(x1)))) -> 1#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     0(0(0(0(x1)))) -> 0(1(1(1(x1))))
     1(0(1(1(x1)))) -> 0(0(0(1(x1))))
    interpretation:
     [1#](x0) = x0,
     
     [0#](x0) = x0,
     
     [1](x0) = 4x0,
     
     [0](x0) = 4x0
    orientation:
     0#(0(0(0(x1)))) = 12x1 >= x1 = 1#(x1)
     
     0#(0(0(0(x1)))) = 12x1 >= 4x1 = 1#(1(x1))
     
     0#(0(0(0(x1)))) = 12x1 >= 8x1 = 1#(1(1(x1)))
     
     0#(0(0(0(x1)))) = 12x1 >= 12x1 = 0#(1(1(1(x1))))
     
     1#(0(1(1(x1)))) = 12x1 >= 4x1 = 0#(1(x1))
     
     1#(0(1(1(x1)))) = 12x1 >= 8x1 = 0#(0(1(x1)))
     
     1#(0(1(1(x1)))) = 12x1 >= 12x1 = 0#(0(0(1(x1))))
     
     0(0(0(0(x1)))) = 16x1 >= 16x1 = 0(1(1(1(x1))))
     
     1(0(1(1(x1)))) = 16x1 >= 16x1 = 0(0(0(1(x1))))
    problem:
     DPs:
      0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
      1#(0(1(1(x1)))) -> 0#(0(0(1(x1))))
     TRS:
      0(0(0(0(x1)))) -> 0(1(1(1(x1))))
      1(0(1(1(x1)))) -> 0(0(0(1(x1))))
    Restore Modifier:
     DPs:
      0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
      1#(0(1(1(x1)))) -> 0#(0(0(1(x1))))
     TRS:
      0(0(0(0(x1)))) -> 0(1(1(1(x1))))
      1(0(1(1(x1)))) -> 0(0(0(1(x1))))
     EDG Processor:
      DPs:
       0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
       1#(0(1(1(x1)))) -> 0#(0(0(1(x1))))
      TRS:
       0(0(0(0(x1)))) -> 0(1(1(1(x1))))
       1(0(1(1(x1)))) -> 0(0(0(1(x1))))
      graph:
       1#(0(1(1(x1)))) -> 0#(0(0(1(x1)))) ->
       0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
       0#(0(0(0(x1)))) -> 0#(1(1(1(x1)))) -> 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 2/4
       DPs:
        0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
       TRS:
        0(0(0(0(x1)))) -> 0(1(1(1(x1))))
        1(0(1(1(x1)))) -> 0(0(0(1(x1))))
       Arctic Interpretation Processor:
        dimension: 3
        usable rules:
         0(0(0(0(x1)))) -> 0(1(1(1(x1))))
         1(0(1(1(x1)))) -> 0(0(0(1(x1))))
        interpretation:
         [0#](x0) = [0 0 0]x0,
         
                   [0 0 0]  
         [1](x0) = [0 0 0]x0
                   [0 0 0]  ,
         
                   [0  -& 0 ]     [-&]
         [0](x0) = [1  0  0 ]x0 + [0 ]
                   [0  0  -&]     [-&]
        orientation:
         0#(0(0(0(x1)))) = [1 1 1]x1 + [0] >= [0 0 0]x1 = 0#(1(1(1(x1))))
         
                          [1 0 1]     [0]    [0 0 0]     [-&]                 
         0(0(0(0(x1)))) = [2 1 1]x1 + [1] >= [1 1 1]x1 + [0 ] = 0(1(1(1(x1))))
                          [1 1 1]     [0]    [0 0 0]     [-&]                 
         
                          [1 1 1]     [0]    [1 1 1]     [0]                 
         1(0(1(1(x1)))) = [1 1 1]x1 + [0] >= [1 1 1]x1 + [0] = 0(0(0(1(x1))))
                          [1 1 1]     [0]    [1 1 1]     [0]                 
        problem:
         DPs:
          
         TRS:
          0(0(0(0(x1)))) -> 0(1(1(1(x1))))
          1(0(1(1(x1)))) -> 0(0(0(1(x1))))
        Qed