YES

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

Proof:
 DP Processor:
  DPs:
   f#(s(0())) -> f#(0())
   f#(+(x,s(0()))) -> f#(x)
   f#(+(x,y)) -> f#(y)
   f#(+(x,y)) -> f#(x)
  TRS:
   f(0()) -> s(0())
   f(s(0())) -> s(s(0()))
   f(s(0())) -> *(s(s(0())),f(0()))
   f(+(x,s(0()))) -> +(s(s(0())),f(x))
   f(+(x,y)) -> *(f(x),f(y))
  EDG Processor:
   DPs:
    f#(s(0())) -> f#(0())
    f#(+(x,s(0()))) -> f#(x)
    f#(+(x,y)) -> f#(y)
    f#(+(x,y)) -> f#(x)
   TRS:
    f(0()) -> s(0())
    f(s(0())) -> s(s(0()))
    f(s(0())) -> *(s(s(0())),f(0()))
    f(+(x,s(0()))) -> +(s(s(0())),f(x))
    f(+(x,y)) -> *(f(x),f(y))
   graph:
    f#(+(x,s(0()))) -> f#(x) -> f#(s(0())) -> f#(0())
    f#(+(x,s(0()))) -> f#(x) -> f#(+(x,s(0()))) -> f#(x)
    f#(+(x,s(0()))) -> f#(x) -> f#(+(x,y)) -> f#(y)
    f#(+(x,s(0()))) -> f#(x) -> f#(+(x,y)) -> f#(x)
    f#(+(x,y)) -> f#(y) -> f#(s(0())) -> f#(0())
    f#(+(x,y)) -> f#(y) -> f#(+(x,s(0()))) -> f#(x)
    f#(+(x,y)) -> f#(y) -> f#(+(x,y)) -> f#(y)
    f#(+(x,y)) -> f#(y) -> f#(+(x,y)) -> f#(x)
    f#(+(x,y)) -> f#(x) -> f#(s(0())) -> f#(0())
    f#(+(x,y)) -> f#(x) -> f#(+(x,s(0()))) -> f#(x)
    f#(+(x,y)) -> f#(x) -> f#(+(x,y)) -> f#(y)
    f#(+(x,y)) -> f#(x) -> f#(+(x,y)) -> f#(x)
   CDG Processor:
    DPs:
     f#(s(0())) -> f#(0())
     f#(+(x,s(0()))) -> f#(x)
     f#(+(x,y)) -> f#(y)
     f#(+(x,y)) -> f#(x)
    TRS:
     f(0()) -> s(0())
     f(s(0())) -> s(s(0()))
     f(s(0())) -> *(s(s(0())),f(0()))
     f(+(x,s(0()))) -> +(s(s(0())),f(x))
     f(+(x,y)) -> *(f(x),f(y))
    graph:
     
    Qed