YES

TRS:

  le(0(),y) -> true()
  le(s(x),0()) -> false()
  le(s(x),s(y)) -> le(x,y)
  pred(s(x)) -> x
  minus(x,0()) -> x
  minus(x,s(y)) -> pred(minus(x,y))
  mod(0(),y) -> 0()
  mod(s(x),0()) -> 0()
  mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
  if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
  if_mod(false(),s(x),s(y)) -> s(x)

max/plus interpretations on N:

  le_A(x1,x2) = max{2, 1, 1}
  le#_A(x1,x2) = max{6, 14, 7}
  0_A = 10
  0#_A = 2
  true_A = 2
  true#_A = 1
  s_A(x1) = max{0, 6 + x1}
  s#_A(x1) = max{0, 3}
  false_A = 2
  false#_A = 1
  pred_A(x1) = max{4, -2 + x1}
  pred#_A(x1) = max{0, 2}
  minus_A(x1,x2) = max{4, 1 + x1, 3}
  minus#_A(x1,x2) = max{2, 2, 3}
  mod_A(x1,x2) = max{10, 3 + x1, 4}
  mod#_A(x1,x2) = max{5, 8 + x1, -1}
  if_mod_A(x1,x2,x3) = max{10, 6, x2, 4}
  if_mod#_A(x1,x2,x3) = max{13, 4, 4 + x2, 6}

precedence:

  mod > le = 0 = if_mod > true = false = minus > s = pred