YES

Problem:
 strict:
  f(x,0()) -> s(x)
  g(x) -> h(x,gen())
  h(0(),x) -> f(x,x)
  a() -> b()
 weak:
  gen() -> s(gen())

Proof:
 Matrix Interpretation Processor: dim=5
  
  interpretation:
           [0]
           [0]
   [gen] = [0]
           [0]
           [0],
   
                 [1 0 0 0 0]     [1 0 1 1 0]  
                 [3 2 0 1 0]     [0 0 2 1 3]  
   [f](x0, x1) = [0 1 0 3 0]x0 + [2 1 0 0 1]x1
                 [1 0 0 0 1]     [1 1 0 0 1]  
                 [2 1 0 0 0]     [0 0 2 1 0]  ,
   
             [1 2 2 1 2]     [1]
             [0 2 2 2 0]     [2]
   [g](x0) = [0 0 0 2 0]x0 + [1]
             [0 2 0 0 0]     [0]
             [2 1 1 1 0]     [0],
   
                 [1 1 0 0 0]     [3 0 1 1 0]     [1]
                 [0 2 0 0 0]     [3 2 3 2 3]     [1]
   [h](x0, x1) = [0 0 0 2 0]x0 + [3 3 2 3 2]x1 + [1]
                 [0 2 0 0 0]     [2 2 2 0 2]     [0]
                 [0 1 1 1 0]     [3 1 3 1 1]     [0],
   
         [1]
         [1]
   [0] = [1]
         [1]
         [0],
   
         [0]
         [0]
   [b] = [0]
         [0]
         [0],
   
         [0]
         [0]
   [a] = [0]
         [0]
         [1],
   
             [1 0 0 0 0]  
             [0 2 0 0 0]  
   [s](x0) = [0 0 0 0 0]x0
             [1 0 0 0 1]  
             [0 0 0 0 0]  
  orientation:
              [1 0 0 0 0]    [3]    [1 0 0 0 0]        
              [3 2 0 1 0]    [3]    [0 2 0 0 0]        
   f(x,0()) = [0 1 0 3 0]x + [3] >= [0 0 0 0 0]x = s(x)
              [1 0 0 0 1]    [2]    [1 0 0 0 1]        
              [2 1 0 0 0]    [3]    [0 0 0 0 0]        
   
          [1 2 2 1 2]    [1]    [1 1 0 0 0]    [1]             
          [0 2 2 2 0]    [2]    [0 2 0 0 0]    [1]             
   g(x) = [0 0 0 2 0]x + [1] >= [0 0 0 2 0]x + [1] = h(x,gen())
          [0 2 0 0 0]    [0]    [0 2 0 0 0]    [0]             
          [2 1 1 1 0]    [0]    [0 1 1 1 0]    [0]             
   
              [3 0 1 1 0]    [3]    [2 0 1 1 0]          
              [3 2 3 2 3]    [3]    [3 2 2 2 3]          
   h(0(),x) = [3 3 2 3 2]x + [3] >= [2 2 0 3 1]x = f(x,x)
              [2 2 2 0 2]    [2]    [2 1 0 0 2]          
              [3 1 3 1 1]    [3]    [2 1 2 1 0]          
   
         [0]    [0]      
         [0]    [0]      
   a() = [0] >= [0] = b()
         [0]    [0]      
         [1]    [0]      
   
           [0]    [0]           
           [0]    [0]           
   gen() = [0] >= [0] = s(gen())
           [0]    [0]           
           [0]    [0]           
  problem:
   strict:
    g(x) -> h(x,gen())
    a() -> b()
   weak:
    gen() -> s(gen())
  Matrix Interpretation Processor: dim=5
   
   interpretation:
            [0]
            [0]
    [gen] = [0]
            [0]
            [0],
    
              [1 0 0 1 0]     [0]
              [0 1 1 0 0]     [1]
    [g](x0) = [0 0 0 0 0]x0 + [0]
              [0 0 0 0 0]     [0]
              [0 0 0 0 0]     [1],
    
                  [1 0 0 0 0]     [1 0 0 0 0]  
                  [0 0 0 0 0]     [0 0 0 0 0]  
    [h](x0, x1) = [0 0 0 0 0]x0 + [0 0 0 0 0]x1
                  [0 0 0 0 0]     [0 0 0 0 0]  
                  [0 0 0 0 0]     [0 0 0 0 0]  ,
    
          [0]
          [0]
    [b] = [0]
          [0]
          [0],
    
          [1]
          [0]
    [a] = [0]
          [0]
          [0],
    
              [1 0 0 0 0]  
              [0 0 0 0 0]  
    [s](x0) = [0 0 0 0 0]x0
              [0 0 0 0 0]  
              [0 0 0 0 0]  
   orientation:
           [1 0 0 1 0]    [0]    [1 0 0 0 0]              
           [0 1 1 0 0]    [1]    [0 0 0 0 0]              
    g(x) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x = h(x,gen())
           [0 0 0 0 0]    [0]    [0 0 0 0 0]              
           [0 0 0 0 0]    [1]    [0 0 0 0 0]              
    
          [1]    [0]      
          [0]    [0]      
    a() = [0] >= [0] = b()
          [0]    [0]      
          [0]    [0]      
    
            [0]    [0]           
            [0]    [0]           
    gen() = [0] >= [0] = s(gen())
            [0]    [0]           
            [0]    [0]           
   problem:
    strict:
     g(x) -> h(x,gen())
    weak:
     gen() -> s(gen())
   Matrix Interpretation Processor: dim=5
    
    interpretation:
             [0]
             [0]
     [gen] = [0]
             [0]
             [1],
     
               [1 1 0 0 0]     [1]
               [1 0 0 0 0]     [0]
     [g](x0) = [0 0 0 0 0]x0 + [0]
               [0 0 0 0 0]     [1]
               [0 0 0 0 0]     [1],
     
                   [1 0 0 0 0]     [1 0 0 0 0]  
                   [0 0 0 0 0]     [0 0 0 0 0]  
     [h](x0, x1) = [0 0 0 0 0]x0 + [0 0 0 0 0]x1
                   [0 0 0 0 0]     [0 0 0 0 1]  
                   [0 0 0 0 0]     [0 0 0 0 0]  ,
     
               [1 0 0 0 0]     [0]
               [0 0 0 0 0]     [0]
     [s](x0) = [0 0 0 0 0]x0 + [0]
               [0 0 0 0 0]     [0]
               [0 0 0 0 0]     [1]
    orientation:
            [1 1 0 0 0]    [1]    [1 0 0 0 0]    [0]             
            [1 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
     g(x) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = h(x,gen())
            [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]             
            [0 0 0 0 0]    [1]    [0 0 0 0 0]    [0]             
     
             [0]    [0]           
             [0]    [0]           
     gen() = [0] >= [0] = s(gen())
             [0]    [0]           
             [1]    [1]           
    problem:
     strict:
      
     weak:
      gen() -> s(gen())
    Qed