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))

linear polynomial interpretations on N:

  +_A(x1,x2) = x1 + x2 + 1
  +#_A(x1,x2) = 1
  0_A = 1
  0#_A = 0
  s_A(x1) = 1
  s#_A(x1) = 0
  *_A(x1,x2) = x1 + 1
  *#_A(x1,x2) = 2
  sum_A(x1) = x1 + 1
  sum#_A(x1) = x1 + 5
  nil_A = 1
  nil#_A = 1
  cons_A(x1,x2) = x1 + x2 + 1
  cons#_A(x1,x2) = 4
  prod_A(x1) = x1 + 1
  prod#_A(x1) = 3

precedence:

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