YES

Problem:
 0(*(x1)) -> *(1(x1))
 1(*(x1)) -> 0(#(x1))
 #(0(x1)) -> 0(#(x1))
 #(1(x1)) -> 1(#(x1))
 #($(x1)) -> *($(x1))
 #(#(x1)) -> #(x1)
 #(*(x1)) -> *(x1)

Proof:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
             [2  -&]  
   [$](x0) = [2  0 ]x0,
   
             [0  3 ]  
   [#](x0) = [-& 2 ]x0,
   
             [0 2]  
   [1](x0) = [0 2]x0,
   
             [1  2 ]  
   [0](x0) = [-& 2 ]x0,
   
             [2  -&]  
   [*](x0) = [0  2 ]x0
  orientation:
              [3 4]      [2 4]             
   0(*(x1)) = [2 4]x1 >= [2 4]x1 = *(1(x1))
   
              [2 4]      [1  4 ]             
   1(*(x1)) = [2 4]x1 >= [-& 4 ]x1 = 0(#(x1))
   
              [1  5 ]      [1  4 ]             
   #(0(x1)) = [-& 4 ]x1 >= [-& 4 ]x1 = 0(#(x1))
   
              [3 5]      [0 4]             
   #(1(x1)) = [2 4]x1 >= [0 4]x1 = 1(#(x1))
   
              [5 3]      [4  -&]             
   #($(x1)) = [4 2]x1 >= [4  2 ]x1 = *($(x1))
   
              [0  5 ]      [0  3 ]          
   #(#(x1)) = [-& 4 ]x1 >= [-& 2 ]x1 = #(x1)
   
              [3 5]      [2  -&]          
   #(*(x1)) = [2 4]x1 >= [0  2 ]x1 = *(x1)
  problem:
   0(*(x1)) -> *(1(x1))
   1(*(x1)) -> 0(#(x1))
   #(0(x1)) -> 0(#(x1))
   #(1(x1)) -> 1(#(x1))
   #($(x1)) -> *($(x1))
   #(#(x1)) -> #(x1)
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [$](x0) = 1x0,
    
    [#](x0) = 8x0,
    
    [1](x0) = 2x0,
    
    [0](x0) = 2x0,
    
    [*](x0) = 8x0
   orientation:
    0(*(x1)) = 10x1 >= 10x1 = *(1(x1))
    
    1(*(x1)) = 10x1 >= 10x1 = 0(#(x1))
    
    #(0(x1)) = 10x1 >= 10x1 = 0(#(x1))
    
    #(1(x1)) = 10x1 >= 10x1 = 1(#(x1))
    
    #($(x1)) = 9x1 >= 9x1 = *($(x1))
    
    #(#(x1)) = 16x1 >= 8x1 = #(x1)
   problem:
    0(*(x1)) -> *(1(x1))
    1(*(x1)) -> 0(#(x1))
    #(0(x1)) -> 0(#(x1))
    #(1(x1)) -> 1(#(x1))
    #($(x1)) -> *($(x1))
   KBO Processor:
    weight function:
     w0 = 1
     w($) = w(#) = w(1) = w(0) = w(*) = 1
    precedence:
     # > 1 > 0 > $ ~ *
    problem:
     
    Qed