YES

Problem:
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 +(s(x),y) -> s(+(x,y))
 double(x) -> +(x,x)

Proof:
 DP Processor:
  DPs:
   double#(s(x)) -> double#(x)
   +#(x,s(y)) -> +#(x,y)
   +#(s(x),y) -> +#(x,y)
   double#(x) -> +#(x,x)
  TRS:
   double(0()) -> 0()
   double(s(x)) -> s(s(double(x)))
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   +(s(x),y) -> s(+(x,y))
   double(x) -> +(x,x)
  TDG Processor:
   DPs:
    double#(s(x)) -> double#(x)
    +#(x,s(y)) -> +#(x,y)
    +#(s(x),y) -> +#(x,y)
    double#(x) -> +#(x,x)
   TRS:
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    +(s(x),y) -> s(+(x,y))
    double(x) -> +(x,x)
   graph:
    +#(s(x),y) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
    +#(s(x),y) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    +#(x,s(y)) -> +#(x,y) -> +#(s(x),y) -> +#(x,y)
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    double#(s(x)) -> double#(x) -> double#(x) -> +#(x,x)
    double#(s(x)) -> double#(x) -> double#(s(x)) -> double#(x)
    double#(x) -> +#(x,x) -> +#(s(x),y) -> +#(x,y)
    double#(x) -> +#(x,x) -> +#(x,s(y)) -> +#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 8/16
    DPs:
     double#(s(x)) -> double#(x)
    TRS:
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     +(s(x),y) -> s(+(x,y))
     double(x) -> +(x,x)
    LPO Processor:
     argument filtering:
      pi(0) = []
      pi(double) = [0]
      pi(s) = [0]
      pi(+) = [0,1]
      pi(double#) = 0
     precedence:
      double > + > double# ~ s ~ 0
     problem:
      DPs:
       
      TRS:
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       +(s(x),y) -> s(+(x,y))
       double(x) -> +(x,x)
     Qed
    
    DPs:
     +#(s(x),y) -> +#(x,y)
     +#(x,s(y)) -> +#(x,y)
    TRS:
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     +(s(x),y) -> s(+(x,y))
     double(x) -> +(x,x)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [+#](x0, x1) = x0 + x1,
      
      [+](x0, x1) = x0 + x1,
      
      [s](x0) = x0 + 1,
      
      [double](x0) = 2x0,
      
      [0] = 0
     orientation:
      +#(s(x),y) = x + y + 1 >= x + y = +#(x,y)
      
      +#(x,s(y)) = x + y + 1 >= x + y = +#(x,y)
      
      double(0()) = 0 >= 0 = 0()
      
      double(s(x)) = 2x + 2 >= 2x + 2 = s(s(double(x)))
      
      +(x,0()) = x >= x = x
      
      +(x,s(y)) = x + y + 1 >= x + y + 1 = s(+(x,y))
      
      +(s(x),y) = x + y + 1 >= x + y + 1 = s(+(x,y))
      
      double(x) = 2x >= 2x = +(x,x)
     problem:
      DPs:
       
      TRS:
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       +(s(x),y) -> s(+(x,y))
       double(x) -> +(x,x)
     Qed