MAYBE

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

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