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))
  SCC Processor:
   #sccs: 1
   #rules: 4
   #arcs: 16/16
   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))
   Matrix Interpretation Processor:
    dimension: 1
    interpretation:
     [f#](x0) = x0 + 1,
     
     [+](x0, x1) = x0 + x1,
     
     [*](x0, x1) = x0,
     
     [s](x0) = x0,
     
     [f](x0) = x0 + 1,
     
     [0] = 1
    orientation:
     f#(s(0())) = 2 >= 2 = f#(0())
     
     f#(+(x,s(0()))) = x + 2 >= x + 1 = f#(x)
     
     f#(+(x,y)) = x + y + 1 >= y + 1 = f#(y)
     
     f#(+(x,y)) = x + y + 1 >= x + 1 = f#(x)
     
     f(0()) = 2 >= 1 = s(0())
     
     f(s(0())) = 2 >= 1 = s(s(0()))
     
     f(s(0())) = 2 >= 1 = *(s(s(0())),f(0()))
     
     f(+(x,s(0()))) = x + 2 >= x + 2 = +(s(s(0())),f(x))
     
     f(+(x,y)) = x + y + 1 >= x + 1 = *(f(x),f(y))
    problem:
     DPs:
      f#(s(0())) -> f#(0())
      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))
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0) = x0,
      
      [+](x0, x1) = x0 + x1 + 1,
      
      [*](x0, x1) = 0,
      
      [s](x0) = x0,
      
      [f](x0) = x0,
      
      [0] = 1
     orientation:
      f#(s(0())) = 1 >= 1 = f#(0())
      
      f#(+(x,y)) = x + y + 1 >= y = f#(y)
      
      f#(+(x,y)) = x + y + 1 >= x = f#(x)
      
      f(0()) = 1 >= 1 = s(0())
      
      f(s(0())) = 1 >= 1 = s(s(0()))
      
      f(s(0())) = 1 >= 0 = *(s(s(0())),f(0()))
      
      f(+(x,s(0()))) = x + 2 >= x + 2 = +(s(s(0())),f(x))
      
      f(+(x,y)) = x + y + 1 >= 0 = *(f(x),f(y))
     problem:
      DPs:
       f#(s(0())) -> f#(0())
      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))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [f#](x0) = x0,
       
       [+](x0, x1) = x1,
       
       [*](x0, x1) = x1,
       
       [s](x0) = 1,
       
       [f](x0) = 1,
       
       [0] = 0
      orientation:
       f#(s(0())) = 1 >= 0 = f#(0())
       
       f(0()) = 1 >= 1 = s(0())
       
       f(s(0())) = 1 >= 1 = s(s(0()))
       
       f(s(0())) = 1 >= 1 = *(s(s(0())),f(0()))
       
       f(+(x,s(0()))) = 1 >= 1 = +(s(s(0())),f(x))
       
       f(+(x,y)) = 1 >= 1 = *(f(x),f(y))
      problem:
       DPs:
        
       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))
      Qed