YES

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)

linear polynomial interpretations on N:

  exp_A(x1,x2) = x1 + 2
  exp#_A(x1,x2) = x1 + x2 + 3
  0_A = 1
  0#_A = 0
  s_A(x1) = x1 + 1
  s#_A(x1) = 0
  *_A(x1,x2) = 1
  *#_A(x1,x2) = x2 + 1
  +_A(x1,x2) = 0
  +#_A(x1,x2) = 0
  -_A(x1,x2) = x1
  -#_A(x1,x2) = 1

precedence:

  exp > 0 = s > * = + = -