YES

Problem:
 app(app(F(),app(app(F(),f),x)),x) -> app(app(F(),app(G(),app(app(F(),f),x))),app(f,x))

Proof:
 Uncurry Processor:
  F2(F2(f,x),x) -> F2(G1(F2(f,x)),app(f,x))
  app(F1(x2),x3) -> F2(x2,x3)
  app(F(),x3) -> F1(x3)
  app(G(),x3) -> G1(x3)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
               [1 0 0]  
    [G1](x0) = [0 0 0]x0
               [0 1 0]  ,
    
                   [1 0 1]     [1 0 0]     [0]
    [F2](x0, x1) = [0 1 1]x0 + [0 0 0]x1 + [1]
                   [1 1 1]     [0 1 1]     [1],
    
               [1 0 1]     [1]
    [F1](x0) = [0 1 0]x0 + [1]
               [0 1 1]     [1],
    
          [1]
    [G] = [0]
          [0],
    
                    [1 0 0]     [1 0 1]     [0]
    [app](x0, x1) = [0 0 1]x0 + [0 1 0]x1 + [1]
                    [1 1 0]     [0 1 1]     [0],
    
          [1]
    [F] = [1]
          [1]
   orientation:
                    [2 1 2]    [2 1 1]    [1]    [2 1 2]    [2 0 1]    [1]                           
    F2(F2(f,x),x) = [1 2 2]f + [0 1 1]x + [3] >= [0 1 1]f + [0 0 0]x + [2] = F2(G1(F2(f,x)),app(f,x))
                    [2 2 3]    [1 2 2]    [3]    [2 2 3]    [1 2 1]    [3]                           
    
                     [1 0 1]     [1 0 1]     [1]    [1 0 1]     [1 0 0]     [0]            
    app(F1(x2),x3) = [0 1 1]x2 + [0 1 0]x3 + [2] >= [0 1 1]x2 + [0 0 0]x3 + [1] = F2(x2,x3)
                     [1 1 1]     [0 1 1]     [2]    [1 1 1]     [0 1 1]     [1]            
    
                  [1 0 1]     [1]    [1 0 1]     [1]         
    app(F(),x3) = [0 1 0]x3 + [2] >= [0 1 0]x3 + [1] = F1(x3)
                  [0 1 1]     [2]    [0 1 1]     [1]         
    
                  [1 0 1]     [1]    [1 0 0]           
    app(G(),x3) = [0 1 0]x3 + [1] >= [0 0 0]x3 = G1(x3)
                  [0 1 1]     [1]    [0 1 0]           
   problem:
    F2(F2(f,x),x) -> F2(G1(F2(f,x)),app(f,x))
    app(F(),x3) -> F1(x3)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                [1 0 0]  
     [G1](x0) = [1 0 0]x0
                [0 0 0]  ,
     
                    [1 0 1]     [1 0 0]     [0]
     [F2](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                    [1 0 0]     [0 0 0]     [1],
     
                [1 0 0]  
     [F1](x0) = [0 0 0]x0
                [0 0 0]  ,
     
                     [1 0 0]     [1 0 0]     [1]
     [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                     [0 1 1]     [0 0 0]     [0],
     
           [1]
     [F] = [1]
           [1]
    orientation:
                     [2 0 1]    [2 0 0]    [1]    [2 0 1]    [2 0 0]    [1]                           
     F2(F2(f,x),x) = [0 0 0]f + [0 0 0]x + [0] >= [0 0 0]f + [0 0 0]x + [0] = F2(G1(F2(f,x)),app(f,x))
                     [1 0 1]    [1 0 0]    [1]    [1 0 1]    [1 0 0]    [1]                           
     
                   [1 0 0]     [2]    [1 0 0]           
     app(F(),x3) = [0 0 0]x3 + [0] >= [0 0 0]x3 = F1(x3)
                   [0 0 0]     [2]    [0 0 0]           
    problem:
     F2(F2(f,x),x) -> F2(G1(F2(f,x)),app(f,x))
    Matrix Interpretation Processor: dim=2
     
     interpretation:
                 [1 0]  
      [G1](x0) = [0 0]x0,
      
                     [2 1]     [1 2]     [0]
      [F2](x0, x1) = [3 0]x0 + [0 0]x1 + [1],
      
                      [1 0]     [1 0]  
      [app](x0, x1) = [1 0]x0 + [0 0]x1
     orientation:
                      [7 2]    [3 6]    [1]    [7 2]    [3 4]    [0]                           
      F2(F2(f,x),x) = [6 3]f + [3 6]x + [1] >= [6 3]f + [3 6]x + [1] = F2(G1(F2(f,x)),app(f,x))
     problem:
      
     Qed