YES

Problem:
 strict:
  f(x) -> s(x)
  f(s(s(x))) -> s(f(f(x)))
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
             [0  -&]  
   [s](x0) = [0  0 ]x0,
   
             [0 0]  
   [f](x0) = [0 0]x0,
   
                [1 1]  
   [rand](x0) = [3 3]x0
  orientation:
          [0 0]     [0  -&]        
   f(x) = [0 0]x >= [0  0 ]x = s(x)
   
                [0 0]     [0 0]              
   f(s(s(x))) = [0 0]x >= [0 0]x = s(f(f(x)))
   
             [1 1]          
   rand(x) = [3 3]x >= x = x
   
             [1 1]     [1 1]              
   rand(x) = [3 3]x >= [3 3]x = rand(s(x))
  problem:
   strict:
    f(x) -> s(x)
    f(s(s(x))) -> s(f(f(x)))
   weak:
    rand(x) -> rand(s(x))
  String Reversal Processor:
   strict:
    f(x) -> s(x)
    s(s(f(x))) -> f(f(s(x)))
   weak:
    rand(x) -> s(rand(x))
   Matrix Interpretation Processor: dim=5
    
    interpretation:
               [1 1 0 0 0]     [0]
               [0 0 0 1 0]     [0]
     [s](x0) = [0 0 0 0 0]x0 + [1]
               [0 1 0 1 0]     [0]
               [1 0 0 0 0]     [0],
     
               [1 1 0 0 0]     [0]
               [0 0 0 1 0]     [1]
     [f](x0) = [0 0 0 0 0]x0 + [1]
               [0 1 0 1 0]     [1]
               [1 0 1 0 0]     [0],
     
                  [1 0 0 0 0]     [1]
                  [0 0 0 0 0]     [0]
     [rand](x0) = [0 0 0 1 0]x0 + [1]
                  [0 0 0 0 0]     [0]
                  [1 0 1 0 1]     [1]
    orientation:
            [1 1 0 0 0]    [0]    [1 1 0 0 0]    [0]       
            [0 0 0 1 0]    [1]    [0 0 0 1 0]    [0]       
     f(x) = [0 0 0 0 0]x + [1] >= [0 0 0 0 0]x + [1] = s(x)
            [0 1 0 1 0]    [1]    [0 1 0 1 0]    [0]       
            [1 0 1 0 0]    [0]    [1 0 0 0 0]    [0]       
     
                  [1 2 0 2 0]    [2]    [1 2 0 2 0]    [1]             
                  [0 1 0 2 0]    [2]    [0 1 0 2 0]    [2]             
     s(s(f(x))) = [0 0 0 0 0]x + [1] >= [0 0 0 0 0]x + [1] = f(f(s(x)))
                  [0 2 0 3 0]    [3]    [0 2 0 3 0]    [3]             
                  [1 1 0 1 0]    [1]    [1 1 0 1 0]    [1]             
     
               [1 0 0 0 0]    [1]    [1 0 0 0 0]    [1]             
               [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
     rand(x) = [0 0 0 1 0]x + [1] >= [0 0 0 0 0]x + [1] = s(rand(x))
               [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
               [1 0 1 0 1]    [1]    [1 0 0 0 0]    [1]             
    problem:
     strict:
      f(x) -> s(x)
     weak:
      rand(x) -> s(rand(x))
    Arctic Interpretation Processor:
     dimension: 4
     interpretation:
                [0  -& -& 0 ]  
                [-& -& -& -&]  
      [s](x0) = [-& -& -& -&]x0
                [-& -& -& -&]  ,
      
                [3 0 0 3]  
                [0 0 0 0]  
      [f](x0) = [0 0 0 0]x0
                [0 0 0 0]  ,
      
                   [0 0 0 0]  
                   [0 0 0 0]  
      [rand](x0) = [0 0 0 0]x0
                   [0 0 0 0]  
     orientation:
             [3 0 0 3]     [0  -& -& 0 ]        
             [0 0 0 0]     [-& -& -& -&]        
      f(x) = [0 0 0 0]x >= [-& -& -& -&]x = s(x)
             [0 0 0 0]     [-& -& -& -&]        
      
                [0 0 0 0]     [0  0  0  0 ]              
                [0 0 0 0]     [-& -& -& -&]              
      rand(x) = [0 0 0 0]x >= [-& -& -& -&]x = s(rand(x))
                [0 0 0 0]     [-& -& -& -&]              
     problem:
      strict:
       
      weak:
       rand(x) -> s(rand(x))
     Qed