YES

TRS:

  le(0(),y) -> true()
  le(s(x),0()) -> false()
  le(s(x),s(y)) -> le(x,y)
  minus(0(),y) -> 0()
  minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
  if_minus(true(),s(x),y) -> 0()
  if_minus(false(),s(x),y) -> s(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{32, 1 + x1, 33}
  le#_A(x1,x2) = max{44, 41, 42}
  0_A = 7
  0#_A = 39
  true_A = 33
  true#_A = 40
  s_A(x1) = max{1, 31 + x1}
  s#_A(x1) = max{46, 53}
  false_A = 33
  false#_A = 43
  minus_A(x1,x2) = max{7, 7 + x1, -1}
  minus#_A(x1,x2) = max{51, 31 + x1, 48}
  if_minus_A(x1,x2,x3) = max{9, 8, 7 + x2, 30}
  if_minus#_A(x1,x2,x3) = max{54, 17 + x1, 7 + x2, 54}
  mod_A(x1,x2) = max{32, 5 + x1, 30}
  mod#_A(x1,x2) = max{0, 23 + x1, 45}
  if_mod_A(x1,x2,x3) = max{30, 31, 2 + x2, 12}
  if_mod#_A(x1,x2,x3) = max{47, 52, x2, 29}

precedence:

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