YES

TRS:

  sqr(0()) -> 0()
  sqr(s(x)) -> +(sqr(x),s(double(x)))
  double(0()) -> 0()
  double(s(x)) -> s(s(double(x)))
  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))
  sqr(s(x)) -> s(+(sqr(x),double(x)))

max/plus interpretations on N:

  sqr_A(x1) = max{9, -5}
  sqr#_A(x1) = max{1, -3}
  0_A = 1
  0#_A = 0
  s_A(x1) = max{3, -4}
  s#_A(x1) = max{0, 1}
  +_A(x1,x2) = max{1, x1, 6 + x2}
  +#_A(x1,x2) = max{1, 1, 1}
  double_A(x1) = max{3, -5}
  double#_A(x1) = max{1, -2}

precedence:

  sqr > + = double > 0 = s