YES

Problem:
 app(app(app(compose(),f),g),x) -> app(g,app(f,x))
 app(reverse(),l) -> app(app(reverse2(),l),nil())
 app(app(reverse2(),nil()),l) -> l
 app(app(reverse2(),app(app(cons(),x),xs)),l) -> app(app(reverse2(),xs),app(app(cons(),x),l))
 app(hd(),app(app(cons(),x),xs)) -> x
 app(tl(),app(app(cons(),x),xs)) -> xs
 last() -> app(app(compose(),hd()),reverse())
 init() -> app(app(compose(),reverse()),app(app(compose(),tl()),reverse()))

Proof:
 Uncurry Processor:
  compose3(f,g,x) -> app(g,app(f,x))
  reverse1(l) -> reverse22(l,nil())
  reverse22(nil(),l) -> l
  reverse22(cons2(x,xs),l) -> reverse22(xs,cons2(x,l))
  hd1(cons2(x,xs)) -> x
  tl1(cons2(x,xs)) -> xs
  last() -> compose2(hd(),reverse())
  init() -> compose2(reverse(),compose2(tl(),reverse()))
  app(compose2(x6,x5),x7) -> compose3(x6,x5,x7)
  app(compose1(x6),x7) -> compose2(x6,x7)
  app(compose(),x7) -> compose1(x7)
  app(reverse(),x7) -> reverse1(x7)
  app(reverse21(x6),x7) -> reverse22(x6,x7)
  app(reverse2(),x7) -> reverse21(x7)
  app(cons1(x6),x7) -> cons2(x6,x7)
  app(cons(),x7) -> cons1(x7)
  app(hd(),x7) -> hd1(x7)
  app(tl(),x7) -> tl1(x7)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [tl1](x0) = x0 + 2,
    
    [hd1](x0) = x0 + 5,
    
    [cons2](x0, x1) = x0 + x1 + 1,
    
    [cons1](x0) = x0 + 4,
    
    [reverse22](x0, x1) = x0 + x1 + 2,
    
    [reverse21](x0) = x0 + 6,
    
    [reverse1](x0) = x0 + 2,
    
    [compose1](x0) = x0,
    
    [compose3](x0, x1, x2) = 2x0 + 2x1 + x2,
    
    [compose2](x0, x1) = x0 + x1,
    
    [init] = 3,
    
    [last] = 5,
    
    [tl] = 1,
    
    [hd] = 4,
    
    [cons] = 4,
    
    [nil] = 0,
    
    [reverse2] = 3,
    
    [reverse] = 1,
    
    [app](x0, x1) = 2x0 + x1,
    
    [compose] = 0
   orientation:
    compose3(f,g,x) = 2f + 2g + x >= 2f + 2g + x = app(g,app(f,x))
    
    reverse1(l) = l + 2 >= l + 2 = reverse22(l,nil())
    
    reverse22(nil(),l) = l + 2 >= l = l
    
    reverse22(cons2(x,xs),l) = l + x + xs + 3 >= l + x + xs + 3 = reverse22(xs,cons2(x,l))
    
    hd1(cons2(x,xs)) = x + xs + 6 >= x = x
    
    tl1(cons2(x,xs)) = x + xs + 3 >= xs = xs
    
    last() = 5 >= 5 = compose2(hd(),reverse())
    
    init() = 3 >= 3 = compose2(reverse(),compose2(tl(),reverse()))
    
    app(compose2(x6,x5),x7) = 2x5 + 2x6 + x7 >= 2x5 + 2x6 + x7 = compose3(x6,x5,x7)
    
    app(compose1(x6),x7) = 2x6 + x7 >= x6 + x7 = compose2(x6,x7)
    
    app(compose(),x7) = x7 >= x7 = compose1(x7)
    
    app(reverse(),x7) = x7 + 2 >= x7 + 2 = reverse1(x7)
    
    app(reverse21(x6),x7) = 2x6 + x7 + 12 >= x6 + x7 + 2 = reverse22(x6,x7)
    
    app(reverse2(),x7) = x7 + 6 >= x7 + 6 = reverse21(x7)
    
    app(cons1(x6),x7) = 2x6 + x7 + 8 >= x6 + x7 + 1 = cons2(x6,x7)
    
    app(cons(),x7) = x7 + 8 >= x7 + 4 = cons1(x7)
    
    app(hd(),x7) = x7 + 8 >= x7 + 5 = hd1(x7)
    
    app(tl(),x7) = x7 + 2 >= x7 + 2 = tl1(x7)
   problem:
    compose3(f,g,x) -> app(g,app(f,x))
    reverse1(l) -> reverse22(l,nil())
    reverse22(cons2(x,xs),l) -> reverse22(xs,cons2(x,l))
    last() -> compose2(hd(),reverse())
    init() -> compose2(reverse(),compose2(tl(),reverse()))
    app(compose2(x6,x5),x7) -> compose3(x6,x5,x7)
    app(compose1(x6),x7) -> compose2(x6,x7)
    app(compose(),x7) -> compose1(x7)
    app(reverse(),x7) -> reverse1(x7)
    app(reverse2(),x7) -> reverse21(x7)
    app(tl(),x7) -> tl1(x7)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 0 0]  
     [tl1](x0) = [0 0 0]x0
                 [0 0 1]  ,
     
                       [1 0 0]     [1 0 0]     [0]
     [cons2](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0]
                       [0 0 0]     [1 1 1]     [1],
     
                           [1 0 0]     [1 0 0]  
     [reverse22](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                           [0 1 1]     [0 1 0]  ,
     
                       [1 0 0]  
     [reverse21](x0) = [0 0 0]x0
                       [0 1 0]  ,
     
                      [1 1 0]  
     [reverse1](x0) = [0 0 0]x0
                      [0 1 1]  ,
     
                      [1 0 0]     [1]
     [compose1](x0) = [0 0 0]x0 + [0]
                      [0 1 1]     [1],
     
                              [1 1 1]     [1 1 0]     [1 1 0]     [1]
     [compose3](x0, x1, x2) = [0 0 0]x0 + [0 1 1]x1 + [0 0 0]x2 + [0]
                              [1 1 1]     [1 1 0]     [0 1 1]     [0],
     
                          [1 0 0]     [1 1 0]     [0]
     [compose2](x0, x1) = [0 1 1]x0 + [0 0 0]x1 + [1]
                          [0 0 0]     [0 1 1]     [0],
     
              [1]
     [init] = [1]
              [1],
     
              [0]
     [last] = [1]
              [1],
     
            [0]
     [tl] = [0]
            [0],
     
            [0]
     [hd] = [0]
            [0],
     
             [0]
     [nil] = [0]
             [0],
     
                  [0]
     [reverse2] = [0]
                  [0],
     
                 [0]
     [reverse] = [0]
                 [0],
     
                     [1 1 0]     [1 1 0]  
     [app](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                     [1 1 0]     [0 1 1]  ,
     
                 [0]
     [compose] = [1]
                 [0]
    orientation:
                       [1 1 1]    [1 1 0]    [1 1 0]    [1]    [1 1 1]    [1 1 0]    [1 1 0]                   
     compose3(f,g,x) = [0 0 0]f + [0 1 1]g + [0 0 0]x + [0] >= [0 0 0]f + [0 0 1]g + [0 0 0]x = app(g,app(f,x))
                       [1 1 1]    [1 1 0]    [0 1 1]    [0]    [1 1 1]    [1 1 0]    [0 1 1]                   
     
                   [1 1 0]     [1 0 0]                      
     reverse1(l) = [0 0 0]l >= [0 0 0]l = reverse22(l,nil())
                   [0 1 1]     [0 1 1]                      
     
                                [1 0 0]    [1 0 0]    [1 0 0]     [0]    [1 0 0]    [1 0 0]    [1 0 0]                             
     reverse22(cons2(x,xs),l) = [0 0 0]l + [0 0 0]x + [0 0 0]xs + [0] >= [0 0 0]l + [0 0 0]x + [0 0 0]xs = reverse22(xs,cons2(x,l))
                                [0 1 0]    [0 0 1]    [1 1 1]     [1]    [0 0 0]    [0 0 1]    [0 1 1]                             
     
              [0]    [0]                           
     last() = [1] >= [1] = compose2(hd(),reverse())
              [1]    [0]                           
     
              [1]    [1]                                               
     init() = [1] >= [1] = compose2(reverse(),compose2(tl(),reverse()))
              [1]    [1]                                               
     
                               [1 1 0]     [1 1 1]     [1 1 0]     [1]    [1 1 0]     [1 1 1]     [1 1 0]     [1]                     
     app(compose2(x6,x5),x7) = [0 1 1]x5 + [0 0 0]x6 + [0 0 0]x7 + [0] >= [0 1 1]x5 + [0 0 0]x6 + [0 0 0]x7 + [0] = compose3(x6,x5,x7)
                               [1 1 0]     [1 1 1]     [0 1 1]     [1]    [1 1 0]     [1 1 1]     [0 1 1]     [0]                     
     
                            [1 0 0]     [1 1 0]     [1]    [1 0 0]     [1 1 0]     [0]                  
     app(compose1(x6),x7) = [0 1 1]x6 + [0 0 0]x7 + [1] >= [0 1 1]x6 + [0 0 0]x7 + [1] = compose2(x6,x7)
                            [1 0 0]     [0 1 1]     [1]    [0 0 0]     [0 1 1]     [0]                  
     
                         [1 1 0]     [1]    [1 0 0]     [1]               
     app(compose(),x7) = [0 0 0]x7 + [0] >= [0 0 0]x7 + [0] = compose1(x7)
                         [0 1 1]     [1]    [0 1 1]     [1]               
     
                         [1 1 0]      [1 1 0]                 
     app(reverse(),x7) = [0 0 0]x7 >= [0 0 0]x7 = reverse1(x7)
                         [0 1 1]      [0 1 1]                 
     
                          [1 1 0]      [1 0 0]                  
     app(reverse2(),x7) = [0 0 0]x7 >= [0 0 0]x7 = reverse21(x7)
                          [0 1 1]      [0 1 0]                  
     
                    [1 1 0]      [1 0 0]            
     app(tl(),x7) = [0 0 0]x7 >= [0 0 0]x7 = tl1(x7)
                    [0 1 1]      [0 0 1]            
    problem:
     reverse1(l) -> reverse22(l,nil())
     reverse22(cons2(x,xs),l) -> reverse22(xs,cons2(x,l))
     last() -> compose2(hd(),reverse())
     init() -> compose2(reverse(),compose2(tl(),reverse()))
     app(compose2(x6,x5),x7) -> compose3(x6,x5,x7)
     app(compose(),x7) -> compose1(x7)
     app(reverse(),x7) -> reverse1(x7)
     app(reverse2(),x7) -> reverse21(x7)
     app(tl(),x7) -> tl1(x7)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                  [1 0 0]     [0]
      [tl1](x0) = [0 0 1]x0 + [0]
                  [0 1 0]     [1],
      
                        [1 0 0]          [0]
      [cons2](x0, x1) = [0 1 1]x0 + x1 + [0]
                        [0 1 1]          [1],
      
                            [1 0 1]     [1 1 0]     [0]
      [reverse22](x0, x1) = [0 0 1]x0 + [0 0 1]x1 + [0]
                            [0 1 0]     [0 1 0]     [1],
      
                        [1 0 1]     [0]
      [reverse21](x0) = [0 0 1]x0 + [0]
                        [0 1 0]     [1],
      
                       [1 0 1]     [1]
      [reverse1](x0) = [0 0 1]x0 + [0]
                       [0 1 0]     [1],
      
                       [1 0 1]     [0]
      [compose1](x0) = [0 0 1]x0 + [0]
                       [0 1 0]     [1],
      
                               [1 0 0]     [1 0 0]     [1 0 1]  
      [compose3](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 1]x2
                               [0 0 0]     [0 0 0]     [0 1 0]  ,
      
                           [1 0 0]     [1 0 0]  
      [compose2](x0, x1) = [0 0 1]x0 + [0 0 0]x1
                           [0 0 0]     [0 1 0]  ,
      
               [1]
      [init] = [1]
               [1],
      
               [1]
      [last] = [0]
               [0],
      
             [0]
      [tl] = [0]
             [1],
      
             [0]
      [hd] = [0]
             [0],
      
              [0]
      [nil] = [0]
              [0],
      
                   [0]
      [reverse2] = [0]
                   [1],
      
                  [0]
      [reverse] = [0]
                  [1],
      
                      [1 0 1]     [1 0 1]     [0]
      [app](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0]
                      [0 0 0]     [0 1 0]     [1],
      
                  [0]
      [compose] = [0]
                  [0]
     orientation:
                    [1 0 1]    [1]    [1 0 1]    [0]                     
      reverse1(l) = [0 0 1]l + [0] >= [0 0 1]l + [0] = reverse22(l,nil())
                    [0 1 0]    [1]    [0 1 0]    [1]                     
      
                                 [1 1 0]    [1 1 1]    [1 0 1]     [1]    [1 1 0]    [1 1 1]    [1 0 1]     [0]                           
      reverse22(cons2(x,xs),l) = [0 0 1]l + [0 1 1]x + [0 0 1]xs + [1] >= [0 0 1]l + [0 1 1]x + [0 0 1]xs + [1] = reverse22(xs,cons2(x,l))
                                 [0 1 0]    [0 1 1]    [0 1 0]     [1]    [0 1 0]    [0 1 1]    [0 1 0]     [1]                           
      
               [1]    [0]                           
      last() = [0] >= [0] = compose2(hd(),reverse())
               [0]    [0]                           
      
               [1]    [0]                                               
      init() = [1] >= [1] = compose2(reverse(),compose2(tl(),reverse()))
               [1]    [1]                                               
      
                                [1 1 0]     [1 0 0]     [1 0 1]     [0]    [1 0 0]     [1 0 0]     [1 0 1]                       
      app(compose2(x6,x5),x7) = [0 0 0]x5 + [0 0 0]x6 + [0 0 1]x7 + [0] >= [0 0 0]x5 + [0 0 0]x6 + [0 0 1]x7 = compose3(x6,x5,x7)
                                [0 0 0]     [0 0 0]     [0 1 0]     [1]    [0 0 0]     [0 0 0]     [0 1 0]                       
      
                          [1 0 1]     [0]    [1 0 1]     [0]               
      app(compose(),x7) = [0 0 1]x7 + [0] >= [0 0 1]x7 + [0] = compose1(x7)
                          [0 1 0]     [1]    [0 1 0]     [1]               
      
                          [1 0 1]     [1]    [1 0 1]     [1]               
      app(reverse(),x7) = [0 0 1]x7 + [0] >= [0 0 1]x7 + [0] = reverse1(x7)
                          [0 1 0]     [1]    [0 1 0]     [1]               
      
                           [1 0 1]     [1]    [1 0 1]     [0]                
      app(reverse2(),x7) = [0 0 1]x7 + [0] >= [0 0 1]x7 + [0] = reverse21(x7)
                           [0 1 0]     [1]    [0 1 0]     [1]                
      
                     [1 0 1]     [1]    [1 0 0]     [0]          
      app(tl(),x7) = [0 0 1]x7 + [0] >= [0 0 1]x7 + [0] = tl1(x7)
                     [0 1 0]     [1]    [0 1 0]     [1]          
     problem:
      app(compose2(x6,x5),x7) -> compose3(x6,x5,x7)
      app(compose(),x7) -> compose1(x7)
      app(reverse(),x7) -> reverse1(x7)
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                        [1 0 0]  
       [reverse1](x0) = [0 0 0]x0
                        [0 0 0]  ,
       
                        [1 0 0]  
       [compose1](x0) = [0 0 0]x0
                        [0 0 0]  ,
       
                                [1 0 0]     [1 0 0]     [1 0 0]  
       [compose3](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                                [0 0 0]     [0 0 0]     [0 0 0]  ,
       
                            [1 0 0]     [1 0 0]  
       [compose2](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                            [0 0 0]     [0 0 0]  ,
       
                   [0]
       [reverse] = [0]
                   [0],
       
                       [1 0 0]     [1 0 0]     [1]
       [app](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                       [0 0 0]     [0 0 0]     [0],
       
                   [0]
       [compose] = [0]
                   [0]
      orientation:
                                 [1 0 0]     [1 0 0]     [1 0 0]     [1]    [1 0 0]     [1 0 0]     [1 0 0]                       
       app(compose2(x6,x5),x7) = [0 0 0]x5 + [0 0 0]x6 + [0 0 0]x7 + [0] >= [0 0 0]x5 + [0 0 0]x6 + [0 0 0]x7 = compose3(x6,x5,x7)
                                 [0 0 0]     [0 0 0]     [0 0 0]     [0]    [0 0 0]     [0 0 0]     [0 0 0]                       
       
                           [1 0 0]     [1]    [1 0 0]                 
       app(compose(),x7) = [0 0 0]x7 + [0] >= [0 0 0]x7 = compose1(x7)
                           [0 0 0]     [0]    [0 0 0]                 
       
                           [1 0 0]     [1]    [1 0 0]                 
       app(reverse(),x7) = [0 0 0]x7 + [0] >= [0 0 0]x7 = reverse1(x7)
                           [0 0 0]     [0]    [0 0 0]                 
      problem:
       
      Qed