YES

Problem:
 app(nil(),y) -> y
 app(add(n,x),y) -> add(n,app(x,y))
 reverse(nil()) -> nil()
 reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
 shuffle(nil()) -> nil()
 shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                   [1 0 0]     [1]
   [shuffle](x0) = [0 0 0]x0 + [0]
                   [1 0 0]     [1],
   
                   [1 0 0]     [0]
   [reverse](x0) = [0 0 0]x0 + [1]
                   [1 0 0]     [1],
   
                   [1 0 0]     [1 0 0]  
   [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [1 0 0]  ,
   
                   [1 0 0]     [1 1 0]     [0]
   [app](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1]
                   [1 0 0]     [1 1 1]     [1],
   
           [0]
   [nil] = [0]
           [0]
  orientation:
                  [1 1 0]    [0]         
   app(nil(),y) = [0 1 0]y + [1] >= y = y
                  [1 1 1]    [1]         
   
                     [1 0 0]    [1 0 0]    [1 1 0]    [0]    [1 0 0]    [1 0 0]    [1 1 0]                   
   app(add(n,x),y) = [0 0 0]n + [0 0 0]x + [0 1 0]y + [1] >= [0 0 0]n + [0 0 0]x + [0 0 0]y = add(n,app(x,y))
                     [1 0 0]    [1 0 0]    [1 1 1]    [1]    [0 0 0]    [1 0 0]    [1 1 0]                   
   
                    [0]    [0]        
   reverse(nil()) = [1] >= [0] = nil()
                    [1]    [0]        
   
                       [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [0]                               
   reverse(add(n,x)) = [0 0 0]n + [0 0 0]x + [1] >= [0 0 0]n + [0 0 0]x + [1] = app(reverse(x),add(n,nil()))
                       [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1]                               
   
                    [1]    [0]        
   shuffle(nil()) = [0] >= [0] = nil()
                    [1]    [0]        
   
                       [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1]                             
   shuffle(add(n,x)) = [0 0 0]n + [0 0 0]x + [0] >= [0 0 0]n + [0 0 0]x + [0] = add(n,shuffle(reverse(x)))
                       [1 0 0]    [1 0 0]    [1]    [0 0 0]    [1 0 0]    [1]                             
  problem:
   app(nil(),y) -> y
   app(add(n,x),y) -> add(n,app(x,y))
   reverse(nil()) -> nil()
   reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
   shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                    [1 1 0]     [0]
    [shuffle](x0) = [0 1 0]x0 + [0]
                    [0 0 0]     [1],
    
                    [1 0 0]  
    [reverse](x0) = [0 1 0]x0
                    [0 0 0]  ,
    
                    [1 0 0]     [1 0 0]     [0]
    [add](x0, x1) = [0 0 1]x0 + [0 1 0]x1 + [1]
                    [0 0 0]     [0 0 0]     [0],
    
                    [1 0 0]     [1 0 1]  
    [app](x0, x1) = [0 1 0]x0 + [0 1 1]x1
                    [0 0 0]     [0 0 1]  ,
    
            [0]
    [nil] = [0]
            [0]
   orientation:
                   [1 0 1]          
    app(nil(),y) = [0 1 1]y >= y = y
                   [0 0 1]          
    
                      [1 0 0]    [1 0 0]    [1 0 1]    [0]    [1 0 0]    [1 0 0]    [1 0 1]    [0]                  
    app(add(n,x),y) = [0 0 1]n + [0 1 0]x + [0 1 1]y + [1] >= [0 0 1]n + [0 1 0]x + [0 1 1]y + [1] = add(n,app(x,y))
                      [0 0 0]    [0 0 0]    [0 0 1]    [0]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                  
    
                     [0]    [0]        
    reverse(nil()) = [0] >= [0] = nil()
                     [0]    [0]        
    
                        [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [0]                               
    reverse(add(n,x)) = [0 0 1]n + [0 1 0]x + [1] >= [0 0 1]n + [0 1 0]x + [1] = app(reverse(x),add(n,nil()))
                        [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]                               
    
                        [1 0 1]    [1 1 0]    [1]    [1 0 0]    [1 1 0]    [0]                             
    shuffle(add(n,x)) = [0 0 1]n + [0 1 0]x + [1] >= [0 0 1]n + [0 1 0]x + [1] = add(n,shuffle(reverse(x)))
                        [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [0]                             
   problem:
    app(nil(),y) -> y
    app(add(n,x),y) -> add(n,app(x,y))
    reverse(nil()) -> nil()
    reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                     [1 0 1]  
     [reverse](x0) = [1 0 0]x0
                     [1 0 1]  ,
     
                     [1 1 0]     [1 0 0]     [1]
     [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                     [0 0 0]     [0 0 1]     [0],
     
                     [1 0 0]       
     [app](x0, x1) = [0 1 0]x0 + x1
                     [1 0 0]       ,
     
             [0]
     [nil] = [0]
             [1]
    orientation:
                              
     app(nil(),y) = y >= y = y
                              
     
                       [1 1 0]    [1 0 0]        [1]    [1 1 0]    [1 0 0]    [1 0 0]    [1]                  
     app(add(n,x),y) = [0 0 0]n + [0 0 0]x + y + [1] >= [0 0 0]n + [0 0 0]x + [0 0 0]y + [1] = add(n,app(x,y))
                       [1 1 0]    [1 0 0]        [1]    [0 0 0]    [1 0 0]    [0 0 1]    [0]                  
     
                      [1]    [0]        
     reverse(nil()) = [0] >= [0] = nil()
                      [1]    [1]        
     
                         [1 1 0]    [1 0 1]    [1]    [1 1 0]    [1 0 1]    [1]                               
     reverse(add(n,x)) = [1 1 0]n + [1 0 0]x + [1] >= [0 0 0]n + [1 0 0]x + [1] = app(reverse(x),add(n,nil()))
                         [1 1 0]    [1 0 1]    [1]    [0 0 0]    [1 0 1]    [1]                               
    problem:
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                      [1 1 1]  
      [reverse](x0) = [0 1 1]x0
                      [0 1 1]  ,
      
                      [1 0 0]     [1 0 0]     [0]
      [add](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0]
                      [0 0 0]     [0 1 0]     [1],
      
                           [1 0 0]  
      [app](x0, x1) = x0 + [0 1 1]x1
                           [0 1 1]  ,
      
              [0]
      [nil] = [0]
              [0]
     orientation:
                     [1 0 0]          
      app(nil(),y) = [0 1 1]y >= y = y
                     [0 1 1]          
      
                        [1 0 0]    [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [1 0 0]    [0]                  
      app(add(n,x),y) = [0 0 0]n + [0 0 1]x + [0 1 1]y + [0] >= [0 0 0]n + [0 0 1]x + [0 1 1]y + [0] = add(n,app(x,y))
                        [0 0 0]    [0 1 0]    [0 1 1]    [1]    [0 0 0]    [0 1 0]    [0 1 1]    [1]                  
      
                          [1 0 0]    [1 1 1]    [1]    [1 0 0]    [1 1 1]    [0]                               
      reverse(add(n,x)) = [0 0 0]n + [0 1 1]x + [1] >= [0 0 0]n + [0 1 1]x + [1] = app(reverse(x),add(n,nil()))
                          [0 0 0]    [0 1 1]    [1]    [0 0 0]    [0 1 1]    [1]                               
     problem:
      app(nil(),y) -> y
      app(add(n,x),y) -> add(n,app(x,y))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
                       [1 0 0]     [1 0 0]     [0]
       [add](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [1]
                       [0 0 0]     [0 1 0]     [0],
       
                       [1 1 1]     [1 0 0]  
       [app](x0, x1) = [0 1 0]x0 + [0 1 1]x1
                       [0 0 1]     [0 1 1]  ,
       
               [1]
       [nil] = [0]
               [0]
      orientation:
                      [1 0 0]    [1]         
       app(nil(),y) = [0 1 1]y + [0] >= y = y
                      [0 1 1]    [0]         
       
                         [1 0 0]    [1 1 1]    [1 0 0]    [1]    [1 0 0]    [1 1 1]    [1 0 0]    [0]                  
       app(add(n,x),y) = [0 0 0]n + [0 0 1]x + [0 1 1]y + [1] >= [0 0 0]n + [0 0 1]x + [0 1 1]y + [1] = add(n,app(x,y))
                         [0 0 0]    [0 1 0]    [0 1 1]    [0]    [0 0 0]    [0 1 0]    [0 1 1]    [0]                  
      problem:
       
      Qed