YES

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

Proof:
 DP Processor:
  DPs:
   exp#(x,s(y)) -> exp#(x,y)
   exp#(x,s(y)) -> *#(x,exp(x,y))
   *#(s(x),y) -> *#(x,y)
   -#(s(x),s(y)) -> -#(x,y)
  TRS:
   exp(x,0()) -> s(0())
   exp(x,s(y)) -> *(x,exp(x,y))
   *(0(),y) -> 0()
   *(s(x),y) -> +(y,*(x,y))
   -(0(),y) -> 0()
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
  Usable Rule Processor:
   DPs:
    exp#(x,s(y)) -> exp#(x,y)
    exp#(x,s(y)) -> *#(x,exp(x,y))
    *#(s(x),y) -> *#(x,y)
    -#(s(x),s(y)) -> -#(x,y)
   TRS:
    f9(x,y) -> x
    f9(x,y) -> y
    exp(x,0()) -> s(0())
    exp(x,s(y)) -> *(x,exp(x,y))
    *(0(),y) -> 0()
    *(s(x),y) -> +(y,*(x,y))
   CDG Processor:
    DPs:
     exp#(x,s(y)) -> exp#(x,y)
     exp#(x,s(y)) -> *#(x,exp(x,y))
     *#(s(x),y) -> *#(x,y)
     -#(s(x),s(y)) -> -#(x,y)
    TRS:
     f9(x,y) -> x
     f9(x,y) -> y
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> *(x,exp(x,y))
     *(0(),y) -> 0()
     *(s(x),y) -> +(y,*(x,y))
    graph:
     -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
     *#(s(x),y) -> *#(x,y) -> *#(s(x),y) -> *#(x,y)
     exp#(x,s(y)) -> *#(x,exp(x,y)) -> *#(s(x),y) -> *#(x,y)
     exp#(x,s(y)) -> exp#(x,y) -> exp#(x,s(y)) -> exp#(x,y)
     exp#(x,s(y)) -> exp#(x,y) -> exp#(x,s(y)) -> *#(x,exp(x,y))
    Restore Modifier:
     DPs:
      exp#(x,s(y)) -> exp#(x,y)
      exp#(x,s(y)) -> *#(x,exp(x,y))
      *#(s(x),y) -> *#(x,y)
      -#(s(x),s(y)) -> -#(x,y)
     TRS:
      exp(x,0()) -> s(0())
      exp(x,s(y)) -> *(x,exp(x,y))
      *(0(),y) -> 0()
      *(s(x),y) -> +(y,*(x,y))
      -(0(),y) -> 0()
      -(x,0()) -> x
      -(s(x),s(y)) -> -(x,y)
     SCC Processor:
      #sccs: 3
      #rules: 3
      #arcs: 5/16
      DPs:
       exp#(x,s(y)) -> exp#(x,y)
      TRS:
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> *(x,exp(x,y))
       *(0(),y) -> 0()
       *(s(x),y) -> +(y,*(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [exp#](x0, x1) = x1 + 1,
        
        [-](x0, x1) = x0 + 1,
        
        [+](x0, x1) = x0,
        
        [*](x0, x1) = x1,
        
        [s](x0) = x0 + 1,
        
        [exp](x0, x1) = 1,
        
        [0] = 0
       orientation:
        exp#(x,s(y)) = y + 2 >= y + 1 = exp#(x,y)
        
        exp(x,0()) = 1 >= 1 = s(0())
        
        exp(x,s(y)) = 1 >= 1 = *(x,exp(x,y))
        
        *(0(),y) = y >= 0 = 0()
        
        *(s(x),y) = y >= y = +(y,*(x,y))
        
        -(0(),y) = 1 >= 0 = 0()
        
        -(x,0()) = x + 1 >= x = x
        
        -(s(x),s(y)) = x + 2 >= x + 1 = -(x,y)
       problem:
        DPs:
         
        TRS:
         exp(x,0()) -> s(0())
         exp(x,s(y)) -> *(x,exp(x,y))
         *(0(),y) -> 0()
         *(s(x),y) -> +(y,*(x,y))
         -(0(),y) -> 0()
         -(x,0()) -> x
         -(s(x),s(y)) -> -(x,y)
       Qed
      
      DPs:
       *#(s(x),y) -> *#(x,y)
      TRS:
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> *(x,exp(x,y))
       *(0(),y) -> 0()
       *(s(x),y) -> +(y,*(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [*#](x0, x1) = x0 + 1,
        
        [-](x0, x1) = x0 + 1,
        
        [+](x0, x1) = x0,
        
        [*](x0, x1) = x1,
        
        [s](x0) = x0 + 1,
        
        [exp](x0, x1) = 1,
        
        [0] = 0
       orientation:
        *#(s(x),y) = x + 2 >= x + 1 = *#(x,y)
        
        exp(x,0()) = 1 >= 1 = s(0())
        
        exp(x,s(y)) = 1 >= 1 = *(x,exp(x,y))
        
        *(0(),y) = y >= 0 = 0()
        
        *(s(x),y) = y >= y = +(y,*(x,y))
        
        -(0(),y) = 1 >= 0 = 0()
        
        -(x,0()) = x + 1 >= x = x
        
        -(s(x),s(y)) = x + 2 >= x + 1 = -(x,y)
       problem:
        DPs:
         
        TRS:
         exp(x,0()) -> s(0())
         exp(x,s(y)) -> *(x,exp(x,y))
         *(0(),y) -> 0()
         *(s(x),y) -> +(y,*(x,y))
         -(0(),y) -> 0()
         -(x,0()) -> x
         -(s(x),s(y)) -> -(x,y)
       Qed
      
      DPs:
       -#(s(x),s(y)) -> -#(x,y)
      TRS:
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> *(x,exp(x,y))
       *(0(),y) -> 0()
       *(s(x),y) -> +(y,*(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [-#](x0, x1) = x1 + 1,
        
        [-](x0, x1) = x0,
        
        [+](x0, x1) = x1,
        
        [*](x0, x1) = x1,
        
        [s](x0) = x0 + 1,
        
        [exp](x0, x1) = 1,
        
        [0] = 0
       orientation:
        -#(s(x),s(y)) = y + 2 >= y + 1 = -#(x,y)
        
        exp(x,0()) = 1 >= 1 = s(0())
        
        exp(x,s(y)) = 1 >= 1 = *(x,exp(x,y))
        
        *(0(),y) = y >= 0 = 0()
        
        *(s(x),y) = y >= y = +(y,*(x,y))
        
        -(0(),y) = 0 >= 0 = 0()
        
        -(x,0()) = x >= x = x
        
        -(s(x),s(y)) = x + 1 >= x = -(x,y)
       problem:
        DPs:
         
        TRS:
         exp(x,0()) -> s(0())
         exp(x,s(y)) -> *(x,exp(x,y))
         *(0(),y) -> 0()
         *(s(x),y) -> +(y,*(x,y))
         -(0(),y) -> 0()
         -(x,0()) -> x
         -(s(x),s(y)) -> -(x,y)
       Qed