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=2
  
  interpretation:
           [1]
   [gen] = [1],
   
                 [2 0]     [1 0]     [2]
   [f](x0, x1) = [0 0]x0 + [0 0]x1 + [0],
   
             [2 0]     [3]
   [g](x0) = [0 0]x0 + [0],
   
                 [2 0]     [3 0]  
   [h](x0, x1) = [0 0]x0 + [0 0]x1,
   
         [1]
   [0] = [0],
   
         [0]
   [b] = [0],
   
         [0]
   [a] = [0],
   
             [1 0]  
   [s](x0) = [0 0]x0
  orientation:
              [2 0]    [3]    [1 0]        
   f(x,0()) = [0 0]x + [0] >= [0 0]x = s(x)
   
          [2 0]    [3]    [2 0]    [3]             
   g(x) = [0 0]x + [0] >= [0 0]x + [0] = h(x,gen())
   
              [3 0]    [2]    [3 0]    [2]         
   h(0(),x) = [0 0]x + [0] >= [0 0]x + [0] = f(x,x)
   
         [0]    [0]      
   a() = [0] >= [0] = b()
   
           [1]    [1]           
   gen() = [1] >= [0] = s(gen())
  problem:
   strict:
    g(x) -> h(x,gen())
    h(0(),x) -> f(x,x)
    a() -> b()
   weak:
    gen() -> s(gen())
  Matrix Interpretation Processor: dim=2
   
   interpretation:
            [0]
    [gen] = [2],
    
                  [2 0]     [1 0]  
    [f](x0, x1) = [0 1]x0 + [0 0]x1,
    
              [3 0]     [0]
    [g](x0) = [0 0]x0 + [2],
    
                  [2 0]     [3 0]  
    [h](x0, x1) = [0 0]x0 + [0 1]x1,
    
          [0]
    [0] = [0],
    
          [0]
    [b] = [0],
    
          [1]
    [a] = [0],
    
              [2 0]  
    [s](x0) = [0 1]x0
   orientation:
           [3 0]    [0]    [2 0]    [0]             
    g(x) = [0 0]x + [2] >= [0 0]x + [2] = h(x,gen())
    
               [3 0]     [3 0]          
    h(0(),x) = [0 1]x >= [0 1]x = f(x,x)
    
          [1]    [0]      
    a() = [0] >= [0] = b()
    
            [0]    [0]           
    gen() = [2] >= [2] = s(gen())
   problem:
    strict:
     g(x) -> h(x,gen())
     h(0(),x) -> f(x,x)
    weak:
     gen() -> s(gen())
   Matrix Interpretation Processor: dim=4
    
    interpretation:
             [0]
             [0]
     [gen] = [0]
             [0],
     
                   [1 0 1 0]     [1 0 1 0]     [0]
                   [0 0 0 0]     [0 0 0 0]     [0]
     [f](x0, x1) = [1 0 0 0]x0 + [1 0 0 0]x1 + [3]
                   [1 2 0 0]     [1 0 0 1]     [0],
     
               [1 1 1 0]     [2]
               [0 0 0 0]     [0]
     [g](x0) = [2 0 0 2]x0 + [1]
               [0 0 0 0]     [2],
     
                   [1 0 0 0]     [3 1 2 0]     [0]
                   [0 0 0 0]     [0 0 0 0]     [0]
     [h](x0, x1) = [0 0 0 2]x0 + [2 0 0 0]x1 + [1]
                   [0 0 0 0]     [3 2 0 1]     [1],
     
           [0]
           [0]
     [0] = [0]
           [1],
     
               [2 0 0 0]  
               [0 0 0 0]  
     [s](x0) = [0 0 0 0]x0
               [0 0 0 0]  
    orientation:
            [1 1 1 0]    [2]    [1 0 0 0]    [0]             
            [0 0 0 0]    [0]    [0 0 0 0]    [0]             
     g(x) = [2 0 0 2]x + [1] >= [0 0 0 2]x + [1] = h(x,gen())
            [0 0 0 0]    [2]    [0 0 0 0]    [1]             
     
                [3 1 2 0]    [0]    [2 0 2 0]    [0]         
                [0 0 0 0]    [0]    [0 0 0 0]    [0]         
     h(0(),x) = [2 0 0 0]x + [3] >= [2 0 0 0]x + [3] = f(x,x)
                [3 2 0 1]    [1]    [2 2 0 1]    [0]         
     
             [0]    [0]           
             [0]    [0]           
     gen() = [0] >= [0] = s(gen())
             [0]    [0]           
    problem:
     strict:
      h(0(),x) -> f(x,x)
     weak:
      gen() -> s(gen())
    Matrix Interpretation Processor: dim=2
     
     interpretation:
              [2]
      [gen] = [1],
      
                    [1 0]     [1 0]  
      [f](x0, x1) = [0 0]x0 + [2 0]x1,
      
                    [1 0]     [3 1]  
      [h](x0, x1) = [2 0]x0 + [2 0]x1,
      
            [1]
      [0] = [0],
      
                [1 0]     [0]
      [s](x0) = [0 0]x0 + [1]
     orientation:
                 [3 1]    [1]    [2 0]          
      h(0(),x) = [2 0]x + [2] >= [2 0]x = f(x,x)
      
              [2]    [2]           
      gen() = [1] >= [1] = s(gen())
     problem:
      strict:
       
      weak:
       gen() -> s(gen())
     Qed