YES

Problem:
 0(0(0(0(x1)))) -> 0(1(1(1(x1))))
 1(0(0(1(x1)))) -> 0(0(0(0(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(0(1(x1)))) -> 0#(x1)
   1#(0(0(1(x1)))) -> 0#(0(x1))
   1#(0(0(1(x1)))) -> 0#(0(0(x1)))
   1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
  TRS:
   0(0(0(0(x1)))) -> 0(1(1(1(x1))))
   1(0(0(1(x1)))) -> 0(0(0(0(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(0(1(x1)))) -> 0#(x1)
    1#(0(0(1(x1)))) -> 0#(0(x1))
    1#(0(0(1(x1)))) -> 0#(0(0(x1)))
    1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
   TRS:
    0(0(0(0(x1)))) -> 0(1(1(1(x1))))
    1(0(0(1(x1)))) -> 0(0(0(0(x1))))
   graph:
    1#(0(0(1(x1)))) -> 0#(0(0(0(x1)))) ->
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
    1#(0(0(1(x1)))) -> 0#(0(0(0(x1)))) ->
    0#(0(0(0(x1)))) -> 1#(1(1(x1)))
    1#(0(0(1(x1)))) -> 0#(0(0(0(x1)))) ->
    0#(0(0(0(x1)))) -> 1#(1(x1))
    1#(0(0(1(x1)))) -> 0#(0(0(0(x1)))) -> 0#(0(0(0(x1)))) -> 1#(x1)
    1#(0(0(1(x1)))) -> 0#(0(0(x1))) ->
    0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
    1#(0(0(1(x1)))) -> 0#(0(0(x1))) ->
    0#(0(0(0(x1)))) -> 1#(1(1(x1)))
    1#(0(0(1(x1)))) -> 0#(0(0(x1))) -> 0#(0(0(0(x1)))) -> 1#(1(x1))
    1#(0(0(1(x1)))) -> 0#(0(0(x1))) -> 0#(0(0(0(x1)))) -> 1#(x1)
    1#(0(0(1(x1)))) -> 0#(0(x1)) -> 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
    1#(0(0(1(x1)))) -> 0#(0(x1)) -> 0#(0(0(0(x1)))) -> 1#(1(1(x1)))
    1#(0(0(1(x1)))) -> 0#(0(x1)) -> 0#(0(0(0(x1)))) -> 1#(1(x1))
    1#(0(0(1(x1)))) -> 0#(0(x1)) -> 0#(0(0(0(x1)))) -> 1#(x1)
    1#(0(0(1(x1)))) -> 0#(x1) -> 0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
    1#(0(0(1(x1)))) -> 0#(x1) -> 0#(0(0(0(x1)))) -> 1#(1(1(x1)))
    1#(0(0(1(x1)))) -> 0#(x1) -> 0#(0(0(0(x1)))) -> 1#(1(x1))
    1#(0(0(1(x1)))) -> 0#(x1) -> 0#(0(0(0(x1)))) -> 1#(x1)
    0#(0(0(0(x1)))) -> 1#(1(1(x1))) ->
    1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
    0#(0(0(0(x1)))) -> 1#(1(1(x1))) ->
    1#(0(0(1(x1)))) -> 0#(0(0(x1)))
    0#(0(0(0(x1)))) -> 1#(1(1(x1))) -> 1#(0(0(1(x1)))) -> 0#(0(x1))
    0#(0(0(0(x1)))) -> 1#(1(1(x1))) -> 1#(0(0(1(x1)))) -> 0#(x1)
    0#(0(0(0(x1)))) -> 1#(1(x1)) -> 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
    0#(0(0(0(x1)))) -> 1#(1(x1)) -> 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
    0#(0(0(0(x1)))) -> 1#(1(x1)) -> 1#(0(0(1(x1)))) -> 0#(0(x1))
    0#(0(0(0(x1)))) -> 1#(1(x1)) -> 1#(0(0(1(x1)))) -> 0#(x1)
    0#(0(0(0(x1)))) -> 1#(x1) -> 1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
    0#(0(0(0(x1)))) -> 1#(x1) -> 1#(0(0(1(x1)))) -> 0#(0(0(x1)))
    0#(0(0(0(x1)))) -> 1#(x1) -> 1#(0(0(1(x1)))) -> 0#(0(x1))
    0#(0(0(0(x1)))) -> 1#(x1) -> 1#(0(0(1(x1)))) -> 0#(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
    interpretation:
     [1#](x0) = x0,
     
     [0#](x0) = x0,
     
     [1](x0) = 1x0,
     
     [0](x0) = 1x0
    orientation:
     0#(0(0(0(x1)))) = 3x1 >= x1 = 1#(x1)
     
     0#(0(0(0(x1)))) = 3x1 >= 1x1 = 1#(1(x1))
     
     0#(0(0(0(x1)))) = 3x1 >= 2x1 = 1#(1(1(x1)))
     
     0#(0(0(0(x1)))) = 3x1 >= 3x1 = 0#(1(1(1(x1))))
     
     1#(0(0(1(x1)))) = 3x1 >= x1 = 0#(x1)
     
     1#(0(0(1(x1)))) = 3x1 >= 1x1 = 0#(0(x1))
     
     1#(0(0(1(x1)))) = 3x1 >= 2x1 = 0#(0(0(x1)))
     
     1#(0(0(1(x1)))) = 3x1 >= 3x1 = 0#(0(0(0(x1))))
     
     0(0(0(0(x1)))) = 4x1 >= 4x1 = 0(1(1(1(x1))))
     
     1(0(0(1(x1)))) = 4x1 >= 4x1 = 0(0(0(0(x1))))
    problem:
     DPs:
      0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
      1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
     TRS:
      0(0(0(0(x1)))) -> 0(1(1(1(x1))))
      1(0(0(1(x1)))) -> 0(0(0(0(x1))))
    EDG Processor:
     DPs:
      0#(0(0(0(x1)))) -> 0#(1(1(1(x1))))
      1#(0(0(1(x1)))) -> 0#(0(0(0(x1))))
     TRS:
      0(0(0(0(x1)))) -> 0(1(1(1(x1))))
      1(0(0(1(x1)))) -> 0(0(0(0(x1))))
     graph:
      1#(0(0(1(x1)))) -> 0#(0(0(0(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(0(1(x1)))) -> 0(0(0(0(x1))))
      Arctic Interpretation Processor:
       dimension: 4
       interpretation:
        [0#](x0) = [0  0  0  -&]x0 + [0],
        
                  [0  0  -& -&]     [0 ]
                  [0  0  -& -&]     [-&]
        [1](x0) = [0  0  -& -&]x0 + [0 ]
                  [0  0  0  0 ]     [0 ],
        
                  [-& 0  -& 0 ]     [0]
                  [0  0  0  0 ]     [0]
        [0](x0) = [0  0  -& 1 ]x0 + [0]
                  [0  -& -& -&]     [0]
       orientation:
        0#(0(0(0(x1)))) = [1 1 0 1]x1 + [1] >= [0  0  -& -&]x1 + [0] = 0#(1(1(1(x1))))
        
                         [1 0 0 1]     [1]    [0  0  0  0 ]     [0]                 
                         [1 1 0 1]     [1]    [0  0  0  0 ]     [0]                 
        0(0(0(0(x1)))) = [1 1 1 1]x1 + [1] >= [1  1  1  1 ]x1 + [1] = 0(1(1(1(x1))))
                         [0 0 0 1]     [0]    [0  0  -& -&]     [0]                 
        
                         [1 1 1 1]     [1]    [1 0 0 1]     [1]                 
                         [1 1 1 1]     [1]    [1 1 0 1]     [1]                 
        1(0(0(1(x1)))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = 0(0(0(0(x1))))
                         [1 1 1 1]     [1]    [0 0 0 1]     [0]                 
       problem:
        DPs:
         
        TRS:
         0(0(0(0(x1)))) -> 0(1(1(1(x1))))
         1(0(0(1(x1)))) -> 0(0(0(0(x1))))
       Qed