MAYBE

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

Proof:
 Complexity Transformation Processor:
  strict:
   0(*(x1)) -> *(1(x1))
   1(*(x1)) -> 0(#(x1))
   #(0(x1)) -> 0(#(x1))
   #(1(x1)) -> 1(#(x1))
   #($(x1)) -> *($(x1))
   #(#(x1)) -> #(x1)
   #(*(x1)) -> *(x1)
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [$](x0) = x0,
     
     [#](x0) = x0,
     
     [1](x0) = x0,
     
     [0](x0) = x0 + 1,
     
     [*](x0) = x0
    orientation:
     0(*(x1)) = x1 + 1 >= x1 = *(1(x1))
     
     1(*(x1)) = x1 >= x1 + 1 = 0(#(x1))
     
     #(0(x1)) = x1 + 1 >= x1 + 1 = 0(#(x1))
     
     #(1(x1)) = x1 >= x1 = 1(#(x1))
     
     #($(x1)) = x1 >= x1 = *($(x1))
     
     #(#(x1)) = x1 >= x1 = #(x1)
     
     #(*(x1)) = x1 >= x1 = *(x1)
    problem:
     strict:
      1(*(x1)) -> 0(#(x1))
      #(0(x1)) -> 0(#(x1))
      #(1(x1)) -> 1(#(x1))
      #($(x1)) -> *($(x1))
      #(#(x1)) -> #(x1)
      #(*(x1)) -> *(x1)
     weak:
      0(*(x1)) -> *(1(x1))
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [$](x0) = x0,
       
       [#](x0) = x0,
       
       [1](x0) = x0,
       
       [0](x0) = x0,
       
       [*](x0) = x0 + 1
      orientation:
       1(*(x1)) = x1 + 1 >= x1 = 0(#(x1))
       
       #(0(x1)) = x1 >= x1 = 0(#(x1))
       
       #(1(x1)) = x1 >= x1 = 1(#(x1))
       
       #($(x1)) = x1 >= x1 + 1 = *($(x1))
       
       #(#(x1)) = x1 >= x1 = #(x1)
       
       #(*(x1)) = x1 + 1 >= x1 + 1 = *(x1)
       
       0(*(x1)) = x1 + 1 >= x1 + 1 = *(1(x1))
      problem:
       strict:
        #(0(x1)) -> 0(#(x1))
        #(1(x1)) -> 1(#(x1))
        #($(x1)) -> *($(x1))
        #(#(x1)) -> #(x1)
        #(*(x1)) -> *(x1)
       weak:
        1(*(x1)) -> 0(#(x1))
        0(*(x1)) -> *(1(x1))
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [$](x0) = x0,
         
         [#](x0) = x0 + 1,
         
         [1](x0) = x0,
         
         [0](x0) = x0,
         
         [*](x0) = x0 + 1
        orientation:
         #(0(x1)) = x1 + 1 >= x1 + 1 = 0(#(x1))
         
         #(1(x1)) = x1 + 1 >= x1 + 1 = 1(#(x1))
         
         #($(x1)) = x1 + 1 >= x1 + 1 = *($(x1))
         
         #(#(x1)) = x1 + 2 >= x1 + 1 = #(x1)
         
         #(*(x1)) = x1 + 2 >= x1 + 1 = *(x1)
         
         1(*(x1)) = x1 + 1 >= x1 + 1 = 0(#(x1))
         
         0(*(x1)) = x1 + 1 >= x1 + 1 = *(1(x1))
        problem:
         strict:
          #(0(x1)) -> 0(#(x1))
          #(1(x1)) -> 1(#(x1))
          #($(x1)) -> *($(x1))
         weak:
          #(#(x1)) -> #(x1)
          #(*(x1)) -> *(x1)
          1(*(x1)) -> 0(#(x1))
          0(*(x1)) -> *(1(x1))
        Matrix Interpretation Processor:
         dimension: 3
         max_matrix:
          [1 1 1]
          [0 1 1]
          [0 0 1]
          interpretation:
                     [1 0 0]     [1]
           [$](x0) = [0 0 0]x0 + [0]
                     [0 0 0]     [0],
           
                     [1 1 0]     [0]
           [#](x0) = [0 1 0]x0 + [0]
                     [0 0 0]     [1],
           
                     [1 1 1]     [0]
           [1](x0) = [0 1 0]x0 + [1]
                     [0 0 1]     [0],
           
                     [1 1 0]     [1]
           [0](x0) = [0 1 0]x0 + [1]
                     [0 0 0]     [1],
           
                     [1 1 0]     [0]
           [*](x0) = [0 1 1]x0 + [0]
                     [0 0 0]     [1]
          orientation:
                      [1 2 0]     [2]    [1 2 0]     [1]           
           #(0(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = 0(#(x1))
                      [0 0 0]     [1]    [0 0 0]     [1]           
           
                      [1 2 1]     [1]    [1 2 0]     [1]           
           #(1(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = 1(#(x1))
                      [0 0 0]     [1]    [0 0 0]     [1]           
           
                      [1 0 0]     [1]    [1 0 0]     [1]           
           #($(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = *($(x1))
                      [0 0 0]     [1]    [0 0 0]     [1]           
           
                      [1 2 0]     [0]    [1 1 0]     [0]        
           #(#(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = #(x1)
                      [0 0 0]     [1]    [0 0 0]     [1]        
           
                      [1 2 1]     [0]    [1 1 0]     [0]        
           #(*(x1)) = [0 1 1]x1 + [0] >= [0 1 1]x1 + [0] = *(x1)
                      [0 0 0]     [1]    [0 0 0]     [1]        
           
                      [1 2 1]     [1]    [1 2 0]     [1]           
           1(*(x1)) = [0 1 1]x1 + [1] >= [0 1 0]x1 + [1] = 0(#(x1))
                      [0 0 0]     [1]    [0 0 0]     [1]           
           
                      [1 2 1]     [1]    [1 2 1]     [1]           
           0(*(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = *(1(x1))
                      [0 0 0]     [1]    [0 0 0]     [1]           
          problem:
           strict:
            #(1(x1)) -> 1(#(x1))
            #($(x1)) -> *($(x1))
           weak:
            #(0(x1)) -> 0(#(x1))
            #(#(x1)) -> #(x1)
            #(*(x1)) -> *(x1)
            1(*(x1)) -> 0(#(x1))
            0(*(x1)) -> *(1(x1))
          Open