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)

linear polynomial interpretations on N:

  le_A(x1,x2) = x2 + 1
  le#_A(x1,x2) = 0
  0_A = 1
  0#_A = 2
  true_A = 1
  true#_A = 2
  s_A(x1) = x1 + 5
  s#_A(x1) = 13
  false_A = 1
  false#_A = 1
  minus_A(x1,x2) = x1 + 1
  minus#_A(x1,x2) = x1 + x2 + 10
  if_minus_A(x1,x2,x3) = x2 + 1
  if_minus#_A(x1,x2,x3) = x2 + x3 + 9
  mod_A(x1,x2) = x1 + x2
  mod#_A(x1,x2) = x1 + x2 + 2
  if_mod_A(x1,x2,x3) = x2 + x3
  if_mod#_A(x1,x2,x3) = x2 + x3 + 1

precedence:

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