YES

TRS:

  minus_active(0(),y) -> 0()
  mark(0()) -> 0()
  minus_active(s(x),s(y)) -> minus_active(x,y)
  mark(s(x)) -> s(mark(x))
  ge_active(x,0()) -> true()
  mark(minus(x,y)) -> minus_active(x,y)
  ge_active(0(),s(y)) -> false()
  mark(ge(x,y)) -> ge_active(x,y)
  ge_active(s(x),s(y)) -> ge_active(x,y)
  mark(div(x,y)) -> div_active(mark(x),y)
  div_active(0(),s(y)) -> 0()
  mark(if(x,y,z)) -> if_active(mark(x),y,z)
  div_active(s(x),s(y)) -> if_active(ge_active(x,y),s(div(minus(x,y),s(y))),0())
  if_active(true(),x,y) -> mark(x)
  minus_active(x,y) -> minus(x,y)
  if_active(false(),x,y) -> mark(y)
  ge_active(x,y) -> ge(x,y)
  if_active(x,y,z) -> if(x,y,z)
  div_active(x,y) -> div(x,y)

max/plus interpretations on N:

  minus_active_A(x1,x2) = max{3, 13, 0}
  minus_active#_A(x1,x2) = max{5, 7, 9}
  0_A = 13
  0#_A = 6
  mark_A(x1) = max{13, 2 + x1}
  mark#_A(x1) = max{34, 36 + x1}
  s_A(x1) = max{71, 19 + x1}
  s#_A(x1) = max{32, 33}
  ge_active_A(x1,x2) = max{1, -37, 2}
  ge_active#_A(x1,x2) = max{2, 4, 1}
  true_A = 2
  true#_A = 3
  minus_A(x1,x2) = max{0, -26, 0}
  minus#_A(x1,x2) = max{9, 8, 4}
  false_A = 2
  false#_A = 5
  ge_A(x1,x2) = max{0, -40, -36}
  ge#_A(x1,x2) = max{0, 0, 0}
  div_A(x1,x2) = max{52, 23 + x1, -1}
  div#_A(x1,x2) = max{59, 65, 44}
  div_active_A(x1,x2) = max{53, 23 + x1, 26}
  div_active#_A(x1,x2) = max{87, 45 + x1, 61}
  if_A(x1,x2,x3) = max{0, 5 + x1, 9 + x2, 39 + x3}
  if#_A(x1,x2,x3) = max{37, 37 + x1, 43 + x2, 45}
  if_active_A(x1,x2,x3) = max{12, 5 + x1, 11 + x2, 41 + x3}
  if_active#_A(x1,x2,x3) = max{65, 38 + x1, 44 + x2, 42 + x3}

precedence:

  div = if > mark > minus_active = s > 0 > div_active > ge_active = minus = if_active > true = false = ge