YES
TRS:
 {    minus(x, 0()) -> x,
  minus(s(x), s(y)) -> minus(x, y),
        double(0()) -> 0(),
       double(s(x)) -> s(s(double(x))),
       plus(0(), y) -> y,
      plus(s(x), y) -> s(plus(x, y)),
      plus(s(x), y) -> s(plus(minus(x, y), double(y))),
      plus(s(x), y) -> plus(x, s(y))}
 DP:
  Strict:
   {minus#(s(x), s(y)) -> minus#(x, y),
         double#(s(x)) -> double#(x),
        plus#(s(x), y) -> minus#(x, y),
        plus#(s(x), y) -> double#(y),
        plus#(s(x), y) -> plus#(x, y),
        plus#(s(x), y) -> plus#(x, s(y)),
        plus#(s(x), y) -> plus#(minus(x, y), double(y))}
  Weak:
  {    minus(x, 0()) -> x,
   minus(s(x), s(y)) -> minus(x, y),
         double(0()) -> 0(),
        double(s(x)) -> s(s(double(x))),
        plus(0(), y) -> y,
       plus(s(x), y) -> s(plus(x, y)),
       plus(s(x), y) -> s(plus(minus(x, y), double(y))),
       plus(s(x), y) -> plus(x, s(y))}
  EDG:
   {(plus#(s(x), y) -> minus#(x, y), minus#(s(x), s(y)) -> minus#(x, y))
    (plus#(s(x), y) -> plus#(x, s(y)), plus#(s(x), y) -> plus#(minus(x, y), double(y)))
    (plus#(s(x), y) -> plus#(x, s(y)), plus#(s(x), y) -> plus#(x, s(y)))
    (plus#(s(x), y) -> plus#(x, s(y)), plus#(s(x), y) -> plus#(x, y))
    (plus#(s(x), y) -> plus#(x, s(y)), plus#(s(x), y) -> double#(y))
    (plus#(s(x), y) -> plus#(x, s(y)), plus#(s(x), y) -> minus#(x, y))
    (plus#(s(x), y) -> double#(y), double#(s(x)) -> double#(x))
    (double#(s(x)) -> double#(x), double#(s(x)) -> double#(x))
    (plus#(s(x), y) -> plus#(minus(x, y), double(y)), plus#(s(x), y) -> minus#(x, y))
    (plus#(s(x), y) -> plus#(minus(x, y), double(y)), plus#(s(x), y) -> double#(y))
    (plus#(s(x), y) -> plus#(minus(x, y), double(y)), plus#(s(x), y) -> plus#(x, y))
    (plus#(s(x), y) -> plus#(minus(x, y), double(y)), plus#(s(x), y) -> plus#(x, s(y)))
    (plus#(s(x), y) -> plus#(minus(x, y), double(y)), plus#(s(x), y) -> plus#(minus(x, y), double(y)))
    (plus#(s(x), y) -> plus#(x, y), plus#(s(x), y) -> minus#(x, y))
    (plus#(s(x), y) -> plus#(x, y), plus#(s(x), y) -> double#(y))
    (plus#(s(x), y) -> plus#(x, y), plus#(s(x), y) -> plus#(x, y))
    (plus#(s(x), y) -> plus#(x, y), plus#(s(x), y) -> plus#(x, s(y)))
    (plus#(s(x), y) -> plus#(x, y), plus#(s(x), y) -> plus#(minus(x, y), double(y)))
    (minus#(s(x), s(y)) -> minus#(x, y), minus#(s(x), s(y)) -> minus#(x, y))}
   SCCS:
    Scc:
     {plus#(s(x), y) -> plus#(x, y),
      plus#(s(x), y) -> plus#(x, s(y)),
      plus#(s(x), y) -> plus#(minus(x, y), double(y))}
    Scc:
     {double#(s(x)) -> double#(x)}
    Scc:
     {minus#(s(x), s(y)) -> minus#(x, y)}
    SCC:
     Strict:
      {plus#(s(x), y) -> plus#(x, y),
       plus#(s(x), y) -> plus#(x, s(y)),
       plus#(s(x), y) -> plus#(minus(x, y), double(y))}
     Weak:
     {    minus(x, 0()) -> x,
      minus(s(x), s(y)) -> minus(x, y),
            double(0()) -> 0(),
           double(s(x)) -> s(s(double(x))),
           plus(0(), y) -> y,
          plus(s(x), y) -> s(plus(x, y)),
          plus(s(x), y) -> s(plus(minus(x, y), double(y))),
          plus(s(x), y) -> plus(x, s(y))}
     POLY:
      Argument Filtering:
       pi(plus#) = 0, pi(plus) = [], pi(double) = [], pi(s) = [0], pi(0) = [], pi(minus) = 0
      Usable Rules:
       {}
      Interpretation:
       [s](x0) = x0 + 1
      Strict:
       {}
      Weak:
       {    minus(x, 0()) -> x,
        minus(s(x), s(y)) -> minus(x, y),
              double(0()) -> 0(),
             double(s(x)) -> s(s(double(x))),
             plus(0(), y) -> y,
            plus(s(x), y) -> s(plus(x, y)),
            plus(s(x), y) -> s(plus(minus(x, y), double(y))),
            plus(s(x), y) -> plus(x, s(y))}
      Qed
    SCC:
     Strict:
      {double#(s(x)) -> double#(x)}
     Weak:
     {    minus(x, 0()) -> x,
      minus(s(x), s(y)) -> minus(x, y),
            double(0()) -> 0(),
           double(s(x)) -> s(s(double(x))),
           plus(0(), y) -> y,
          plus(s(x), y) -> s(plus(x, y)),
          plus(s(x), y) -> s(plus(minus(x, y), double(y))),
          plus(s(x), y) -> plus(x, s(y))}
     SPSC:
      Simple Projection:
       pi(double#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {minus#(s(x), s(y)) -> minus#(x, y)}
     Weak:
     {    minus(x, 0()) -> x,
      minus(s(x), s(y)) -> minus(x, y),
            double(0()) -> 0(),
           double(s(x)) -> s(s(double(x))),
           plus(0(), y) -> y,
          plus(s(x), y) -> s(plus(x, y)),
          plus(s(x), y) -> s(plus(minus(x, y), double(y))),
          plus(s(x), y) -> plus(x, s(y))}
     SPSC:
      Simple Projection:
       pi(minus#) = 0
      Strict:
       {}
      Qed