YES

TRS:

  -(0(),y) -> 0()
  -(x,0()) -> x
  -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0())
  p(0()) -> 0()
  p(s(x)) -> x

max/plus interpretations on N:

  -_A(x1,x2) = max{1, 14 + x1, 4 + x2}
  -#_A(x1,x2) = max{5, 4, 4 + x2}
  0_A = 1
  0#_A = 0
  s_A(x1) = max{3, 9 + x1}
  s#_A(x1) = max{2, 3}
  if_A(x1,x2,x3) = max{14, 14, -10 + x2, 14}
  if#_A(x1,x2,x3) = max{13, 4 + x1, 3, 12}
  greater_A(x1,x2) = max{9, -1, 9}
  greater#_A(x1,x2) = max{13, 3, 0}
  p_A(x1) = max{2, -4 + x1}
  p#_A(x1) = max{13, 1}

precedence:

  - > s = if = greater > p > 0