YES

Problem:
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(x))) -> s(half(x))
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)
 if(0(),y,z) -> y
 if(s(x),y,z) -> z
 half(double(x)) -> x

Proof:
 DP Processor:
  DPs:
   double#(s(x)) -> double#(x)
   half#(s(s(x))) -> half#(x)
   -#(s(x),s(y)) -> -#(x,y)
  TRS:
   double(0()) -> 0()
   double(s(x)) -> s(s(double(x)))
   half(0()) -> 0()
   half(s(0())) -> 0()
   half(s(s(x))) -> s(half(x))
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
   if(0(),y,z) -> y
   if(s(x),y,z) -> z
   half(double(x)) -> x
  TDG Processor:
   DPs:
    double#(s(x)) -> double#(x)
    half#(s(s(x))) -> half#(x)
    -#(s(x),s(y)) -> -#(x,y)
   TRS:
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
    half(0()) -> 0()
    half(s(0())) -> 0()
    half(s(s(x))) -> s(half(x))
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
    if(0(),y,z) -> y
    if(s(x),y,z) -> z
    half(double(x)) -> x
   graph:
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
    half#(s(s(x))) -> half#(x) -> half#(s(s(x))) -> half#(x)
    double#(s(x)) -> double#(x) -> double#(s(x)) -> double#(x)
   CDG Processor:
    DPs:
     double#(s(x)) -> double#(x)
     half#(s(s(x))) -> half#(x)
     -#(s(x),s(y)) -> -#(x,y)
    TRS:
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     half(0()) -> 0()
     half(s(0())) -> 0()
     half(s(s(x))) -> s(half(x))
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
     if(0(),y,z) -> y
     if(s(x),y,z) -> z
     half(double(x)) -> x
    graph:
     
    Qed