YES

TRS:

  +(x,0()) -> x
  +(0(),x) -> x
  +(s(x),s(y)) -> s(s(+(x,y)))
  +(+(x,y),z) -> +(x,+(y,z))
  *(x,0()) -> 0()
  *(0(),x) -> 0()
  *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
  *(*(x,y),z) -> *(x,*(y,z))
  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{9, 2 + x1, x2}
  +#_A(x1,x2) = max{0, 2, 13}
  0_A = 10
  0#_A = 1
  s_A(x1) = max{10, -1}
  s#_A(x1) = max{5, -1}
  *_A(x1,x2) = max{10, 9, 9}
  *#_A(x1,x2) = max{13, 3, 4}
  sum_A(x1) = max{9, 3 + x1}
  sum#_A(x1) = max{14, 16}
  nil_A = 7
  nil#_A = 6
  cons_A(x1,x2) = max{5, -1 + x1, 5 + x2}
  cons#_A(x1,x2) = max{17, -1, 1 + x2}
  prod_A(x1) = max{10, 9}
  prod#_A(x1) = max{2, -2}

precedence:

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