YES

Problem:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 quot(0(),s(y)) -> 0()
 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
 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)))
 concat(leaf(),y) -> y
 concat(cons(u,v),y) -> cons(u,concat(v,y))
 less_leaves(x,leaf()) -> false()
 less_leaves(leaf(),cons(w,z)) -> true()
 less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
   app#(add(n,x),y) -> app#(x,y)
   reverse#(add(n,x)) -> reverse#(x)
   reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
   shuffle#(add(n,x)) -> reverse#(x)
   shuffle#(add(n,x)) -> shuffle#(reverse(x))
   concat#(cons(u,v),y) -> concat#(v,y)
   less_leaves#(cons(u,v),cons(w,z)) -> concat#(w,z)
   less_leaves#(cons(u,v),cons(w,z)) -> concat#(u,v)
   less_leaves#(cons(u,v),cons(w,z)) -> less_leaves#(concat(u,v),concat(w,z))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   quot(0(),s(y)) -> 0()
   quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
   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)))
   concat(leaf(),y) -> y
   concat(cons(u,v),y) -> cons(u,concat(v,y))
   less_leaves(x,leaf()) -> false()
   less_leaves(leaf(),cons(w,z)) -> true()
   less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
  Usable Rule Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    app#(add(n,x),y) -> app#(x,y)
    reverse#(add(n,x)) -> reverse#(x)
    reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
    shuffle#(add(n,x)) -> reverse#(x)
    shuffle#(add(n,x)) -> shuffle#(reverse(x))
    concat#(cons(u,v),y) -> concat#(v,y)
    less_leaves#(cons(u,v),cons(w,z)) -> concat#(w,z)
    less_leaves#(cons(u,v),cons(w,z)) -> concat#(u,v)
    less_leaves#(cons(u,v),cons(w,z)) -> less_leaves#(concat(u,v),concat(w,z))
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    reverse(nil()) -> nil()
    reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
    app(nil(),y) -> y
    app(add(n,x),y) -> add(n,app(x,y))
    concat(leaf(),y) -> y
    concat(cons(u,v),y) -> cons(u,concat(v,y))
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     reverse(nil()) -> nil()
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
     concat(leaf(),y) -> y
     concat(cons(u,v),y) -> cons(u,concat(v,y))
    interpretation:
     [less_leaves#](x0, x1) = 2x0 + 3/2x1 + 1/2,
     
     [concat#](x0, x1) = x0,
     
     [shuffle#](x0) = 1/2x0 + 7/2,
     
     [reverse#](x0) = 1/2x0 + 7/2,
     
     [app#](x0, x1) = 1/2x0 + 2x1,
     
     [quot#](x0, x1) = 1/2x0 + 2x1,
     
     [minus#](x0, x1) = 3/2x0 + 3,
     
     [cons](x0, x1) = 3x0 + x1 + 2,
     
     [concat](x0, x1) = x0 + x1,
     
     [leaf] = 0,
     
     [reverse](x0) = x0,
     
     [add](x0, x1) = x1 + 1,
     
     [app](x0, x1) = x0 + x1,
     
     [nil] = 0,
     
     [s](x0) = 3x0 + 2,
     
     [minus](x0, x1) = 2x0,
     
     [0] = 0
    orientation:
     minus#(s(x),s(y)) = 9/2x + 6 >= 3/2x + 3 = minus#(x,y)
     
     quot#(s(x),s(y)) = 3/2x + 6y + 5 >= 3/2x + 3 = minus#(x,y)
     
     quot#(s(x),s(y)) = 3/2x + 6y + 5 >= x + 6y + 4 = quot#(minus(x,y),s(y))
     
     app#(add(n,x),y) = 1/2x + 2y + 1/2 >= 1/2x + 2y = app#(x,y)
     
     reverse#(add(n,x)) = 1/2x + 4 >= 1/2x + 7/2 = reverse#(x)
     
     reverse#(add(n,x)) = 1/2x + 4 >= 1/2x + 2 = app#(reverse(x),add(n,nil()))
     
     shuffle#(add(n,x)) = 1/2x + 4 >= 1/2x + 7/2 = reverse#(x)
     
     shuffle#(add(n,x)) = 1/2x + 4 >= 1/2x + 7/2 = shuffle#(reverse(x))
     
     concat#(cons(u,v),y) = 3u + v + 2 >= v = concat#(v,y)
     
     less_leaves#(cons(u,v),cons(w,z)) = 6u + 2v + 9/2w + 3/2z + 15/2 >= w = concat#(w,z)
     
     less_leaves#(cons(u,v),cons(w,z)) = 6u + 2v + 9/2w + 3/2z + 15/2 >= u = concat#(u,v)
     
     less_leaves#(cons(u,v),cons(w,z)) = 6u + 2v + 9/2w + 3/2z + 15/2 >= 2u + 2v + 3/2w + 3/2z + 1/2 = less_leaves#(concat(u,v),concat(w,z))
     
     minus(x,0()) = 2x >= x = x
     
     minus(s(x),s(y)) = 6x + 4 >= 2x = minus(x,y)
     
     reverse(nil()) = 0 >= 0 = nil()
     
     reverse(add(n,x)) = x + 1 >= x + 1 = app(reverse(x),add(n,nil()))
     
     app(nil(),y) = y >= y = y
     
     app(add(n,x),y) = x + y + 1 >= x + y + 1 = add(n,app(x,y))
     
     concat(leaf(),y) = y >= y = y
     
     concat(cons(u,v),y) = 3u + v + y + 2 >= 3u + v + y + 2 = cons(u,concat(v,y))
    problem:
     DPs:
      
     TRS:
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      reverse(nil()) -> nil()
      reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
      app(nil(),y) -> y
      app(add(n,x),y) -> add(n,app(x,y))
      concat(leaf(),y) -> y
      concat(cons(u,v),y) -> cons(u,concat(v,y))
    Qed