YES

TRS:

  p(0()) -> 0()
  p(s(x)) -> x
  le(0(),y) -> true()
  le(s(x),0()) -> false()
  le(s(x),s(y)) -> le(x,y)
  minus(x,y) -> if(le(x,y),x,y)
  if(true(),x,y) -> 0()
  if(false(),x,y) -> s(minus(p(x),y))

max/plus interpretations on N:

  p_A(x1) = max{2, -6 + x1}
  p#_A(x1) = max{0, 5 + x1}
  0_A = 2
  0#_A = 6
  s_A(x1) = max{13, 6 + x1}
  s#_A(x1) = max{13, 2}
  le_A(x1,x2) = max{3, x1, -1}
  le#_A(x1,x2) = max{0, 3, 8}
  true_A = 3
  true#_A = 7
  false_A = 13
  false#_A = 1
  minus_A(x1,x2) = max{0, 6 + x1, 4}
  minus#_A(x1,x2) = max{4, 11 + x1, 13}
  if_A(x1,x2,x3) = max{5, 1 + x1, 6 + x2, 0}
  if#_A(x1,x2,x3) = max{3, x1, 5 + x2, 3}

precedence:

  if > p = s = minus > le > true = false > 0