YES

Problem:
 sort(nil()) -> nil()
 sort(cons(x,y)) -> insert(x,sort(y))
 insert(x,nil()) -> cons(x,nil())
 insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
 choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
 choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
 choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)

Proof:
 DP Processor:
  DPs:
   sort#(cons(x,y)) -> sort#(y)
   sort#(cons(x,y)) -> insert#(x,sort(y))
   insert#(x,cons(v,w)) -> choose#(x,cons(v,w),x,v)
   choose#(x,cons(v,w),0(),s(z)) -> insert#(x,w)
   choose#(x,cons(v,w),s(y),s(z)) -> choose#(x,cons(v,w),y,z)
  TRS:
   sort(nil()) -> nil()
   sort(cons(x,y)) -> insert(x,sort(y))
   insert(x,nil()) -> cons(x,nil())
   insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
   choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
   choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
   choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
  Matrix Interpretation Processor: dim=3
   
   usable rules:
    sort(nil()) -> nil()
    sort(cons(x,y)) -> insert(x,sort(y))
    insert(x,nil()) -> cons(x,nil())
    insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
    choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
    choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
    choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
   interpretation:
    [choose#](x0, x1, x2, x3) = [1 0 0]x1 + [1 0 0]x3,
    
    [insert#](x0, x1) = [0 1 0]x1,
    
    [sort#](x0) = [0 0 1]x0,
    
              [1 1 0]     [1]
    [s](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [0],
    
          [0]
    [0] = [0]
          [0],
    
                               [1 0 0]     [0 1 0]     [0]
    [choose](x0, x1, x2, x3) = [1 0 0]x0 + [0 1 0]x1 + [1]
                               [1 0 0]     [0 0 1]     [1],
    
                       [1 0 0]     [0 1 0]     [1]
    [insert](x0, x1) = [1 0 0]x0 + [0 1 0]x1 + [1]
                       [1 0 0]     [0 0 1]     [1],
    
                     [0 0 0]     [0 1 0]     [0]
    [cons](x0, x1) = [1 0 0]x0 + [0 1 0]x1 + [1]
                     [1 0 0]     [0 0 1]     [1],
    
                 [0 1 1]     [1]
    [sort](x0) = [0 0 1]x0 + [0]
                 [0 1 0]     [1],
    
            [0]
    [nil] = [1]
            [1]
   orientation:
    sort#(cons(x,y)) = [1 0 0]x + [0 0 1]y + [1] >= [0 0 1]y = sort#(y)
    
    sort#(cons(x,y)) = [1 0 0]x + [0 0 1]y + [1] >= [0 0 1]y = insert#(x,sort(y))
    
    insert#(x,cons(v,w)) = [1 0 0]v + [0 1 0]w + [1] >= [1 0 0]v + [0 1 0]w = choose#(x,cons(v,w),x,v)
    
    choose#(x,cons(v,w),0(),s(z)) = [0 1 0]w + [1 1 0]z + [1] >= [0 1 0]w = insert#(x,w)
    
    choose#(x,cons(v,w),s(y),s(z)) = [0 1 0]w + [1 1 0]z + [1] >= [0 1 0]w + [1 0 0]z = choose#(x,cons(v,w),y,z)
    
                  [3]    [0]        
    sort(nil()) = [1] >= [1] = nil()
                  [2]    [1]        
    
                      [2 0 0]    [0 1 1]    [3]    [1 0 0]    [0 0 1]    [1]                    
    sort(cons(x,y)) = [1 0 0]x + [0 0 1]y + [1] >= [1 0 0]x + [0 0 1]y + [1] = insert(x,sort(y))
                      [1 0 0]    [0 1 0]    [2]    [1 0 0]    [0 1 0]    [2]                    
    
                      [1 0 0]    [2]    [0 0 0]    [1]                
    insert(x,nil()) = [1 0 0]x + [2] >= [1 0 0]x + [2] = cons(x,nil())
                      [1 0 0]    [2]    [1 0 0]    [2]                
    
                          [1 0 0]    [0 1 0]    [1 0 0]    [2]    [1 0 0]    [0 1 0]    [1 0 0]    [1]                          
    insert(x,cons(v,w)) = [1 0 0]v + [0 1 0]w + [1 0 0]x + [2] >= [1 0 0]v + [0 1 0]w + [1 0 0]x + [2] = choose(x,cons(v,w),x,v)
                          [1 0 0]    [0 0 1]    [1 0 0]    [2]    [1 0 0]    [0 0 1]    [1 0 0]    [2]                          
    
                                [1 0 0]    [0 1 0]    [1 0 0]    [1]    [1 0 0]    [0 1 0]    [0 0 0]    [1]                    
    choose(x,cons(v,w),y,0()) = [1 0 0]v + [0 1 0]w + [1 0 0]x + [2] >= [1 0 0]v + [0 1 0]w + [1 0 0]x + [2] = cons(x,cons(v,w))
                                [1 0 0]    [0 0 1]    [1 0 0]    [2]    [1 0 0]    [0 0 1]    [1 0 0]    [2]                    
    
                                   [1 0 0]    [0 1 0]    [1 0 0]    [1]    [0 0 0]    [0 1 0]    [1 0 0]    [1]                      
    choose(x,cons(v,w),0(),s(z)) = [1 0 0]v + [0 1 0]w + [1 0 0]x + [2] >= [1 0 0]v + [0 1 0]w + [1 0 0]x + [2] = cons(v,insert(x,w))
                                   [1 0 0]    [0 0 1]    [1 0 0]    [2]    [1 0 0]    [0 0 1]    [1 0 0]    [2]                      
    
                                    [1 0 0]    [0 1 0]    [1 0 0]    [1]    [1 0 0]    [0 1 0]    [1 0 0]    [1]                          
    choose(x,cons(v,w),s(y),s(z)) = [1 0 0]v + [0 1 0]w + [1 0 0]x + [2] >= [1 0 0]v + [0 1 0]w + [1 0 0]x + [2] = choose(x,cons(v,w),y,z)
                                    [1 0 0]    [0 0 1]    [1 0 0]    [2]    [1 0 0]    [0 0 1]    [1 0 0]    [2]                          
   problem:
    DPs:
     
    TRS:
     sort(nil()) -> nil()
     sort(cons(x,y)) -> insert(x,sort(y))
     insert(x,nil()) -> cons(x,nil())
     insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
     choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
     choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
     choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
   Qed