YES

TRS:

  cond1(true(),x) -> cond2(even(x),x)
  cond2(true(),x) -> cond1(neq(x,0()),div2(x))
  cond2(false(),x) -> cond1(neq(x,0()),p(x))
  neq(0(),0()) -> false()
  neq(0(),s(x)) -> true()
  neq(s(x),0()) -> true()
  neq(s(x),s(y())) -> neq(x,y())
  even(0()) -> true()
  even(s(0())) -> false()
  even(s(s(x))) -> even(x)
  div2(0()) -> 0()
  div2(s(0())) -> 0()
  div2(s(s(x))) -> s(div2(x))
  p(0()) -> 0()
  p(s(x)) -> x

max/plus interpretations on N:

  cond1_A(x1,x2) = max{0, 3 + x1, 6 + x2}
  cond1#_A(x1,x2) = max{0, -3 + x1, -3 + x2}
  true_A = 5
  true#_A = 6
  cond2_A(x1,x2) = max{8, 1, 3 + x2}
  cond2#_A(x1,x2) = max{1, -7, -3 + x2}
  even_A(x1) = max{5, 1}
  even#_A(x1) = max{2, 1}
  neq_A(x1,x2) = max{3, -1 + x1, -1 + x2}
  neq#_A(x1,x2) = max{1, -8, 0}
  0_A = 2
  0#_A = 6
  div2_A(x1) = max{2, -3 + x1}
  div2#_A(x1) = max{1, -8}
  false_A = 2
  false#_A = 6
  p_A(x1) = max{2, -3 + x1}
  p#_A(x1) = max{1, -8}
  s_A(x1) = max{3, 7 + x1}
  s#_A(x1) = max{10, 3 + x1}
  y_A = 4
  y#_A = 11

precedence:

  cond1 > cond2 = s > even = div2 = y > true = 0 = false > neq = p