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