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)
  TDG 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)
   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)) -> *#(x,exp(x,y))
    exp#(x,s(y)) -> exp#(x,y) -> exp#(x,s(y)) -> exp#(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)
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(exp) = [0,1]
      pi(s) = [0]
      pi(*) = 0
      pi(+) = 1
      pi(-) = [0]
      pi(exp#) = 1
     weight function:
      w0 = 1
      w(exp#) = w(s) = w(0) = 1
      w(-) = w(+) = w(*) = w(exp) = 0
     precedence:
      - > exp > exp# ~ + ~ * ~ s ~ 0
     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)
    KBO Processor:
     argument filtering:
      pi(0) = []
      pi(exp) = [0,1]
      pi(s) = [0]
      pi(*) = [1]
      pi(+) = 1
      pi(-) = 0
      pi(*#) = 0
     weight function:
      w0 = 1
      w(*#) = w(-) = w(+) = w(s) = w(0) = 1
      w(*) = w(exp) = 0
     precedence:
      *# ~ * ~ exp > - ~ + ~ s ~ 0
     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)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [-#](x0, x1) = x0 + x1,
      
      [-](x0, x1) = 4x0 + 5x1,
      
      [+](x0, x1) = x1,
      
      [*](x0, x1) = 4x0,
      
      [s](x0) = 1x0,
      
      [exp](x0, x1) = 5x0 + 6x1 + 0,
      
      [0] = 0
     orientation:
      -#(s(x),s(y)) = 1x + 1y >= x + y = -#(x,y)
      
      exp(x,0()) = 5x + 6 >= 1 = s(0())
      
      exp(x,s(y)) = 5x + 7y + 0 >= 4x = *(x,exp(x,y))
      
      *(0(),y) = 4 >= 0 = 0()
      
      *(s(x),y) = 5x >= 4x = +(y,*(x,y))
      
      -(0(),y) = 5y + 4 >= 0 = 0()
      
      -(x,0()) = 4x + 5 >= x = x
      
      -(s(x),s(y)) = 5x + 6y >= 4x + 5y = -(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