YES

TRS:

  sum(0()) -> 0()
  sum(s(x)) -> +(sum(x),s(x))
  sum1(0()) -> 0()
  sum1(s(x)) -> s(+(sum1(x),+(x,x)))

max/plus interpretations on N:

  sum_A(x1) = max{1, 3 + x1}
  sum#_A(x1) = max{0, 2}
  0_A = 7
  0#_A = 1
  s_A(x1) = max{7, 16 + x1}
  s#_A(x1) = max{3, -1}
  +_A(x1,x2) = max{11, 2, 3 + x2}
  +#_A(x1,x2) = max{2, 2, 2}
  sum1_A(x1) = max{6, 14 + x1}
  sum1#_A(x1) = max{4, -2}

precedence:

  sum > 0 > sum1 > s > +