YES

Problem:
 strict:
  g(s(x)) -> f(x)
  f(0()) -> s(0())
  f(s(x)) -> s(s(g(x)))
  g(0()) -> 0()
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [rand](x0) = 8x0,
   
   [g](x0) = x0,
   
   [0] = 12,
   
   [s](x0) = x0,
   
   [f](x0) = x0
  orientation:
   g(s(x)) = x >= x = f(x)
   
   f(0()) = 12 >= 12 = s(0())
   
   f(s(x)) = x >= x = s(s(g(x)))
   
   g(0()) = 12 >= 12 = 0()
   
   rand(x) = 8x >= x = x
   
   rand(x) = 8x >= 8x = rand(s(x))
  problem:
   strict:
    g(s(x)) -> f(x)
    f(0()) -> s(0())
    f(s(x)) -> s(s(g(x)))
    g(0()) -> 0()
   weak:
    rand(x) -> rand(s(x))
  Arctic Interpretation Processor:
   dimension: 2
   interpretation:
                 [4 3]  
    [rand](x0) = [1 0]x0,
    
              [3  -&]  
    [g](x0) = [7  -&]x0,
    
          [1]
    [0] = [6],
    
              [0  -&]  
    [s](x0) = [1  -&]x0,
    
              [3  -&]  
    [f](x0) = [7  -&]x0
   orientation:
              [3  -&]     [3  -&]        
    g(s(x)) = [7  -&]x >= [7  -&]x = f(x)
    
             [4]    [1]         
    f(0()) = [8] >= [2] = s(0())
    
              [3  -&]     [3  -&]              
    f(s(x)) = [7  -&]x >= [4  -&]x = s(s(g(x)))
    
             [4]    [1]      
    g(0()) = [8] >= [6] = 0()
    
              [4 3]     [4  -&]              
    rand(x) = [1 0]x >= [1  -&]x = rand(s(x))
   problem:
    strict:
     g(s(x)) -> f(x)
     f(s(x)) -> s(s(g(x)))
    weak:
     rand(x) -> rand(s(x))
   String Reversal Processor:
    strict:
     s(g(x)) -> f(x)
     s(f(x)) -> g(s(s(x)))
    weak:
     rand(x) -> s(rand(x))
    Matrix Interpretation Processor: dim=5
     
     interpretation:
                   [1 0 0 0 1]     [0]
                   [1 0 0 1 1]     [1]
      [rand](x0) = [0 0 0 0 0]x0 + [0]
                   [0 0 0 0 0]     [0]
                   [0 0 0 0 0]     [0],
      
                [1 0 0 0 0]     [0]
                [0 0 0 0 0]     [0]
      [g](x0) = [0 0 1 1 0]x0 + [0]
                [0 0 0 1 0]     [0]
                [0 0 0 0 1]     [1],
      
                [1 0 0 1 1]  
                [1 0 0 0 0]  
      [s](x0) = [0 0 0 0 1]x0
                [0 0 0 1 0]  
                [0 0 1 0 1]  ,
      
                [1 0 0 1 1]     [0]
                [1 0 0 0 0]     [0]
      [f](x0) = [0 0 0 0 1]x0 + [1]
                [0 0 0 1 0]     [0]
                [0 0 1 1 1]     [0]
     orientation:
                [1 0 0 1 1]    [1]    [1 0 0 1 1]    [0]       
                [1 0 0 0 0]    [0]    [1 0 0 0 0]    [0]       
      s(g(x)) = [0 0 0 0 1]x + [1] >= [0 0 0 0 1]x + [1] = f(x)
                [0 0 0 1 0]    [0]    [0 0 0 1 0]    [0]       
                [0 0 1 1 1]    [1]    [0 0 1 1 1]    [0]       
      
                [1 0 1 3 2]    [0]    [1 0 1 2 2]    [0]             
                [1 0 0 1 1]    [0]    [0 0 0 0 0]    [0]             
      s(f(x)) = [0 0 1 1 1]x + [0] >= [0 0 1 1 1]x + [0] = g(s(s(x)))
                [0 0 0 1 0]    [0]    [0 0 0 1 0]    [0]             
                [0 0 1 1 2]    [1]    [0 0 1 0 2]    [1]             
      
                [1 0 0 0 1]    [0]    [1 0 0 0 1]              
                [1 0 0 1 1]    [1]    [1 0 0 0 1]              
      rand(x) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x = s(rand(x))
                [0 0 0 0 0]    [0]    [0 0 0 0 0]              
                [0 0 0 0 0]    [0]    [0 0 0 0 0]              
     problem:
      strict:
       s(f(x)) -> g(s(s(x)))
      weak:
       rand(x) -> s(rand(x))
     Arctic Interpretation Processor:
      dimension: 3
      interpretation:
                    [2  3  0 ]  
       [rand](x0) = [0  -& 0 ]x0
                    [0  -& 0 ]  ,
       
                 [0  -& -&]  
       [g](x0) = [-& -& 0 ]x0
                 [-& -& -&]  ,
       
                 [0  0  0 ]  
       [s](x0) = [-& 0  0 ]x0
                 [-& 0  -&]  ,
       
                 [1  1  0 ]  
       [f](x0) = [0  0  0 ]x0
                 [-& 2  1 ]  
      orientation:
                 [1 2 1]     [0  0  0 ]              
       s(f(x)) = [0 2 1]x >= [-& 0  0 ]x = g(s(s(x)))
                 [0 0 0]     [-& -& -&]              
       
                 [2  3  0 ]     [2  3  0 ]              
       rand(x) = [0  -& 0 ]x >= [0  -& 0 ]x = s(rand(x))
                 [0  -& 0 ]     [0  -& 0 ]              
      problem:
       strict:
        
       weak:
        rand(x) -> s(rand(x))
      Qed