YES

Problem:
 1(2(1(x1))) -> 2(0(2(x1)))
 0(2(1(x1))) -> 1(0(2(x1)))
 L(2(1(x1))) -> L(1(0(2(x1))))
 1(2(0(x1))) -> 2(0(1(x1)))
 1(2(R(x1))) -> 2(0(1(R(x1))))
 0(2(0(x1))) -> 1(0(1(x1)))
 L(2(0(x1))) -> L(1(0(1(x1))))
 0(2(R(x1))) -> 1(0(1(R(x1))))

Proof:
 DP Processor:
  DPs:
   1#(2(1(x1))) -> 0#(2(x1))
   0#(2(1(x1))) -> 0#(2(x1))
   0#(2(1(x1))) -> 1#(0(2(x1)))
   L#(2(1(x1))) -> 0#(2(x1))
   L#(2(1(x1))) -> 1#(0(2(x1)))
   L#(2(1(x1))) -> L#(1(0(2(x1))))
   1#(2(0(x1))) -> 1#(x1)
   1#(2(0(x1))) -> 0#(1(x1))
   1#(2(R(x1))) -> 1#(R(x1))
   1#(2(R(x1))) -> 0#(1(R(x1)))
   0#(2(0(x1))) -> 1#(x1)
   0#(2(0(x1))) -> 0#(1(x1))
   0#(2(0(x1))) -> 1#(0(1(x1)))
   L#(2(0(x1))) -> 1#(x1)
   L#(2(0(x1))) -> 0#(1(x1))
   L#(2(0(x1))) -> 1#(0(1(x1)))
   L#(2(0(x1))) -> L#(1(0(1(x1))))
   0#(2(R(x1))) -> 1#(R(x1))
   0#(2(R(x1))) -> 0#(1(R(x1)))
   0#(2(R(x1))) -> 1#(0(1(R(x1))))
  TRS:
   1(2(1(x1))) -> 2(0(2(x1)))
   0(2(1(x1))) -> 1(0(2(x1)))
   L(2(1(x1))) -> L(1(0(2(x1))))
   1(2(0(x1))) -> 2(0(1(x1)))
   1(2(R(x1))) -> 2(0(1(R(x1))))
   0(2(0(x1))) -> 1(0(1(x1)))
   L(2(0(x1))) -> L(1(0(1(x1))))
   0(2(R(x1))) -> 1(0(1(R(x1))))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
    [L#](x0) = [1 0 0]x0,
    
    [0#](x0) = [1 0 0]x0,
    
    [1#](x0) = [1 0 0]x0,
    
              [0 1 1]     [0]
    [R](x0) = [1 0 1]x0 + [1]
              [1 1 0]     [1],
    
              [0 0 0]     [1]
    [L](x0) = [1 0 0]x0 + [1]
              [0 0 0]     [0],
    
              [0 0 0]     [1]
    [0](x0) = [0 0 0]x0 + [1]
              [1 0 0]     [0],
    
              [1 1 1]  
    [2](x0) = [0 0 0]x0
              [0 0 0]  ,
    
              [1 0 0]     [0]
    [1](x0) = [0 0 0]x0 + [1]
              [0 1 1]     [1]
   orientation:
    1#(2(1(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 = 0#(2(x1))
    
    0#(2(1(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 = 0#(2(x1))
    
    0#(2(1(x1))) = [1 1 1]x1 + [2] >= [1] = 1#(0(2(x1)))
    
    L#(2(1(x1))) = [1 1 1]x1 + [2] >= [1 1 1]x1 = 0#(2(x1))
    
    L#(2(1(x1))) = [1 1 1]x1 + [2] >= [1] = 1#(0(2(x1)))
    
    L#(2(1(x1))) = [1 1 1]x1 + [2] >= [1] = L#(1(0(2(x1))))
    
    1#(2(0(x1))) = [1 0 0]x1 + [2] >= [1 0 0]x1 = 1#(x1)
    
    1#(2(0(x1))) = [1 0 0]x1 + [2] >= [1 0 0]x1 = 0#(1(x1))
    
    1#(2(R(x1))) = [2 2 2]x1 + [2] >= [0 1 1]x1 = 1#(R(x1))
    
    1#(2(R(x1))) = [2 2 2]x1 + [2] >= [0 1 1]x1 = 0#(1(R(x1)))
    
    0#(2(0(x1))) = [1 0 0]x1 + [2] >= [1 0 0]x1 = 1#(x1)
    
    0#(2(0(x1))) = [1 0 0]x1 + [2] >= [1 0 0]x1 = 0#(1(x1))
    
    0#(2(0(x1))) = [1 0 0]x1 + [2] >= [1] = 1#(0(1(x1)))
    
    L#(2(0(x1))) = [1 0 0]x1 + [2] >= [1 0 0]x1 = 1#(x1)
    
    L#(2(0(x1))) = [1 0 0]x1 + [2] >= [1 0 0]x1 = 0#(1(x1))
    
    L#(2(0(x1))) = [1 0 0]x1 + [2] >= [1] = 1#(0(1(x1)))
    
    L#(2(0(x1))) = [1 0 0]x1 + [2] >= [1] = L#(1(0(1(x1))))
    
    0#(2(R(x1))) = [2 2 2]x1 + [2] >= [0 1 1]x1 = 1#(R(x1))
    
    0#(2(R(x1))) = [2 2 2]x1 + [2] >= [0 1 1]x1 = 0#(1(R(x1)))
    
    0#(2(R(x1))) = [2 2 2]x1 + [2] >= [1] = 1#(0(1(R(x1))))
    
                  [1 1 1]     [2]    [1 1 1]     [2]              
    1(2(1(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = 2(0(2(x1)))
                  [0 0 0]     [1]    [0 0 0]     [0]              
    
                  [0 0 0]     [1]    [0 0 0]     [1]              
    0(2(1(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = 1(0(2(x1)))
                  [1 1 1]     [2]    [1 1 1]     [2]              
    
                  [0 0 0]     [1]    [1]                 
    L(2(1(x1))) = [1 1 1]x1 + [3] >= [2] = L(1(0(2(x1))))
                  [0 0 0]     [0]    [0]                 
    
                  [1 0 0]     [2]    [1 0 0]     [2]              
    1(2(0(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = 2(0(1(x1)))
                  [0 0 0]     [1]    [0 0 0]     [0]              
    
                  [2 2 2]     [2]    [0 1 1]     [2]                 
    1(2(R(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = 2(0(1(R(x1))))
                  [0 0 0]     [1]    [0 0 0]     [0]                 
    
                  [0 0 0]     [1]    [0 0 0]     [1]              
    0(2(0(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = 1(0(1(x1)))
                  [1 0 0]     [2]    [1 0 0]     [2]              
    
                  [0 0 0]     [1]    [1]                 
    L(2(0(x1))) = [1 0 0]x1 + [3] >= [2] = L(1(0(1(x1))))
                  [0 0 0]     [0]    [0]                 
    
                  [0 0 0]     [1]    [0 0 0]     [1]                 
    0(2(R(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = 1(0(1(R(x1))))
                  [2 2 2]     [2]    [0 1 1]     [2]                 
   problem:
    DPs:
     
    TRS:
     1(2(1(x1))) -> 2(0(2(x1)))
     0(2(1(x1))) -> 1(0(2(x1)))
     L(2(1(x1))) -> L(1(0(2(x1))))
     1(2(0(x1))) -> 2(0(1(x1)))
     1(2(R(x1))) -> 2(0(1(R(x1))))
     0(2(0(x1))) -> 1(0(1(x1)))
     L(2(0(x1))) -> L(1(0(1(x1))))
     0(2(R(x1))) -> 1(0(1(R(x1))))
   Qed