YES

TRS:

  prime(0()) -> false()
  prime(s(0())) -> false()
  prime(s(s(x))) -> prime1(s(s(x)),s(x))
  prime1(x,0()) -> false()
  prime1(x,s(0())) -> true()
  prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
  divp(x,y) -> =(rem(x,y),0())

max/plus interpretations on N:

  prime_A(x1) = max{0, 2 + x1}
  prime#_A(x1) = max{13, 3 + x1}
  0_A = 1
  0#_A = 6
  false_A = 2
  false#_A = 7
  s_A(x1) = max{6, x1}
  s#_A(x1) = max{8, 4}
  prime1_A(x1,x2) = max{1, 2 + x1, -1}
  prime1#_A(x1,x2) = max{2, 12, 3 + x2}
  true_A = 2
  true#_A = 5
  and_A(x1,x2) = max{1, 2, -1 + x2}
  and#_A(x1,x2) = max{12, 11 + x1, 2}
  not_A(x1) = max{1, -11 + x1}
  not#_A(x1) = max{12, 12}
  divp_A(x1,x2) = max{10, 3 + x1, 1}
  divp#_A(x1,x2) = max{12, 1, 1}
  =_A(x1,x2) = max{4, 1, 4}
  =#_A(x1,x2) = max{0, 0, 0}
  rem_A(x1,x2) = max{1, 1 + x1, 1 + x2}
  rem#_A(x1,x2) = max{0, 0, 0}

precedence:

  prime > 0 = s > true > prime1 > false = and = not = divp > = = rem