YES

TRS:

  le(0(),y) -> true()
  le(s(x),0()) -> false()
  le(s(x),s(y)) -> le(x,y)
  minus(x,0()) -> x
  minus(s(x),s(y)) -> 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{5, 1, 18 + x2}
  le#_A(x1,x2) = max{11, 9, 13}
  0_A = 20
  0#_A = 25
  true_A = 6
  true#_A = 14
  s_A(x1) = max{8, 22 + x1}
  s#_A(x1) = max{27, 29}
  false_A = 18
  false#_A = 28
  minus_A(x1,x2) = max{11, 4 + x1, -1}
  minus#_A(x1,x2) = max{0, -6 + x1, 1}
  mod_A(x1,x2) = max{0, 3 + x1, 19 + x2}
  mod#_A(x1,x2) = max{10, 4 + x1, 10}
  if_mod_A(x1,x2,x3) = max{1, 26, x2, 19 + x3}
  if_mod#_A(x1,x2,x3) = max{9, 8 + x1, -6 + x2, 11}

precedence:

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