YES

TRS:

  sum(0()) -> 0()
  sum(s(x)) -> +(sqr(s(x)),sum(x))
  sqr(x) -> *(x,x)
  sum(s(x)) -> +(*(s(x),s(x)),sum(x))

linear polynomial interpretations on N:

  sum_A(x1) = 1
  sum#_A(x1) = 2
  0_A = 1
  0#_A = 0
  s_A(x1) = x1 + 1
  s#_A(x1) = x1 + 1
  +_A(x1,x2) = 0
  +#_A(x1,x2) = 0
  sqr_A(x1) = x1
  sqr#_A(x1) = 1
  *_A(x1,x2) = 0
  *#_A(x1,x2) = 0

precedence:

  0 > sum = + > s = sqr > *