MAYBE

Problem:
 app(nil(),xs) -> nil()
 app(cons(x,xs),ys) -> cons(x,app(xs,ys))
 rev(nil()) -> nil()
 rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
 shuffle(nil()) -> nil()
 shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                   [1 0 1]  
   [shuffle](x0) = [0 1 0]x0
                   [0 0 1]  ,
   
                      [1 0 0]     [1 0 0]  
   [append](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                      [0 0 0]     [0 0 0]  ,
   
               [1 0 0]     [1]
   [rev](x0) = [0 1 0]x0 + [0]
               [0 0 0]     [0],
   
                    [1 0 0]     [1 0 0]     [0]
   [cons](x0, x1) = [1 0 0]x0 + [0 0 0]x1 + [0]
                    [0 0 0]     [0 1 0]     [1],
   
                   [1 0 0]     [1 1 1]     [0]
   [app](x0, x1) = [1 0 0]x0 + [0 0 0]x1 + [0]
                   [1 0 0]     [0 0 0]     [1],
   
           [0]
   [nil] = [0]
           [0]
  orientation:
                   [1 1 1]     [0]    [0]        
   app(nil(),xs) = [0 0 0]xs + [0] >= [0] = nil()
                   [0 0 0]     [1]    [0]        
   
                        [1 0 0]    [1 0 0]     [1 1 1]     [0]    [1 0 0]    [1 0 0]     [1 1 1]     [0]                     
   app(cons(x,xs),ys) = [1 0 0]x + [1 0 0]xs + [0 0 0]ys + [0] >= [1 0 0]x + [0 0 0]xs + [0 0 0]ys + [0] = cons(x,app(xs,ys))
                        [1 0 0]    [1 0 0]     [0 0 0]     [1]    [0 0 0]    [1 0 0]     [0 0 0]     [1]                     
   
                [1]    [0]        
   rev(nil()) = [0] >= [0] = nil()
                [0]    [0]        
   
                     [1 0 0]    [1 0 0]     [1]    [1 0 0]    [1 0 0]     [1]                                
   rev(cons(x,xs)) = [1 0 0]x + [0 0 0]xs + [0] >= [0 0 0]x + [0 0 0]xs + [0] = append(xs,rev(cons(x,nil())))
                     [0 0 0]    [0 0 0]     [0]    [0 0 0]    [0 0 0]     [0]                                
   
                    [0]    [0]        
   shuffle(nil()) = [0] >= [0] = nil()
                    [0]    [0]        
   
                         [1 0 0]    [1 1 0]     [1]    [1 0 0]    [1 0 0]     [1]                           
   shuffle(cons(x,xs)) = [1 0 0]x + [0 0 0]xs + [0] >= [1 0 0]x + [0 0 0]xs + [0] = cons(x,shuffle(rev(xs)))
                         [0 0 0]    [0 1 0]     [1]    [0 0 0]    [0 1 0]     [1]                           
  problem:
   app(nil(),xs) -> nil()
   app(cons(x,xs),ys) -> cons(x,app(xs,ys))
   rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
   shuffle(nil()) -> nil()
   shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [shuffle](x0) = 4x0 + 2,
    
    [append](x0, x1) = x0 + x1,
    
    [rev](x0) = x0,
    
    [cons](x0, x1) = 2x0 + x1,
    
    [app](x0, x1) = 2x0 + x1 + 4,
    
    [nil] = 0
   orientation:
    app(nil(),xs) = xs + 4 >= 0 = nil()
    
    app(cons(x,xs),ys) = 4x + 2xs + ys + 4 >= 2x + 2xs + ys + 4 = cons(x,app(xs,ys))
    
    rev(cons(x,xs)) = 2x + xs >= 2x + xs = append(xs,rev(cons(x,nil())))
    
    shuffle(nil()) = 2 >= 0 = nil()
    
    shuffle(cons(x,xs)) = 8x + 4xs + 2 >= 2x + 4xs + 2 = cons(x,shuffle(rev(xs)))
   problem:
    app(cons(x,xs),ys) -> cons(x,app(xs,ys))
    rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
    shuffle(cons(x,xs)) -> cons(x,shuffle(rev(xs)))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [shuffle](x0) = 4x0,
     
     [append](x0, x1) = x0 + x1,
     
     [rev](x0) = x0,
     
     [cons](x0, x1) = x0 + x1 + 2,
     
     [app](x0, x1) = x0 + 4x1 + 1,
     
     [nil] = 0
    orientation:
     app(cons(x,xs),ys) = x + xs + 4ys + 3 >= x + xs + 4ys + 3 = cons(x,app(xs,ys))
     
     rev(cons(x,xs)) = x + xs + 2 >= x + xs + 2 = append(xs,rev(cons(x,nil())))
     
     shuffle(cons(x,xs)) = 4x + 4xs + 8 >= x + 4xs + 2 = cons(x,shuffle(rev(xs)))
    problem:
     app(cons(x,xs),ys) -> cons(x,app(xs,ys))
     rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                         [1 0 0]     [1 0 0]  
      [append](x0, x1) = [1 0 0]x0 + [0 0 1]x1
                         [1 0 0]     [0 1 0]  ,
      
                  [1 0 0]     [1]
      [rev](x0) = [1 0 1]x0 + [0]
                  [1 0 1]     [0],
      
                       [1 0 0]     [1 0 0]     [0]
      [cons](x0, x1) = [0 1 1]x0 + [0 1 0]x1 + [1]
                       [0 1 1]     [0 0 0]     [0],
      
                      [1 1 0]     [1 1 1]  
      [app](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                      [1 0 1]     [0 1 0]  ,
      
              [0]
      [nil] = [0]
              [0]
     orientation:
                           [1 1 1]    [1 1 0]     [1 1 1]     [1]    [1 0 0]    [1 1 0]     [1 1 1]     [0]                     
      app(cons(x,xs),ys) = [0 1 1]x + [0 1 0]xs + [0 0 0]ys + [1] >= [0 1 1]x + [0 1 0]xs + [0 0 0]ys + [1] = cons(x,app(xs,ys))
                           [1 1 1]    [1 0 0]     [0 1 0]     [0]    [0 1 1]    [0 0 0]     [0 0 0]     [0]                     
      
                        [1 0 0]    [1 0 0]     [1]    [1 0 0]    [1 0 0]     [1]                                
      rev(cons(x,xs)) = [1 1 1]x + [1 0 0]xs + [0] >= [1 1 1]x + [1 0 0]xs + [0] = append(xs,rev(cons(x,nil())))
                        [1 1 1]    [1 0 0]     [0]    [1 1 1]    [1 0 0]     [0]                                
     problem:
      rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
     DP Processor:
      DPs:
       rev#(cons(x,xs)) -> rev#(cons(x,nil()))
      TRS:
       rev(cons(x,xs)) -> append(xs,rev(cons(x,nil())))
      Open