YES

TRS:

  +(x,0()) -> x
  +(0(),x) -> x
  +(s(x),s(y)) -> s(s(+(x,y)))
  *(x,0()) -> 0()
  *(0(),x) -> 0()
  *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
  sum(nil()) -> 0()
  sum(cons(x,l)) -> +(x,sum(l))
  prod(nil()) -> s(0())
  prod(cons(x,l)) -> *(x,prod(l))

max/plus interpretations on N:

  +_A(x1,x2) = max{41, x1, 13 + x2}
  +#_A(x1,x2) = max{35, 36, 36}
  0_A = 29
  0#_A = 32
  s_A(x1) = max{1, x1}
  s#_A(x1) = max{36, 36}
  *_A(x1,x2) = max{54, 28 + x1, 26 + x2}
  *#_A(x1,x2) = max{34, 37, 40 + x2}
  sum_A(x1) = max{28, 1 + x1}
  sum#_A(x1) = max{37, 38}
  nil_A = 30
  nil#_A = 37
  cons_A(x1,x2) = max{55, 37 + x1, 39 + x2}
  cons#_A(x1,x2) = max{0, 0, 0}
  prod_A(x1) = max{13, -1 + x1}
  prod#_A(x1) = max{33, 1 + x1}

precedence:

  cons > prod > * = sum = nil > + = 0 > s