YES

TRS:

  cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
  and(true(),true()) -> true()
  and(x,false()) -> false()
  and(false(),x) -> false()
  gr(0(),0()) -> false()
  gr(0(),x) -> false()
  gr(s(x),0()) -> true()
  gr(s(x),s(y)) -> gr(x,y)
  p(0()) -> 0()
  p(s(x)) -> x

max/plus interpretations on N:

  cond_A(x1,x2,x3,x4) = max{0, 0, 1, 2, x4}
  cond#_A(x1,x2,x3,x4) = max{0, -4 + x1, x2, x3, 0}
  true_A = 10
  true#_A = 1
  and_A(x1,x2) = max{3, x1, -2 + x2}
  and#_A(x1,x2) = max{6, -1, 2}
  gr_A(x1,x2) = max{3, 1 + x1, 1}
  gr#_A(x1,x2) = max{2, 6, 0}
  p_A(x1) = max{1, -1 + x1}
  p#_A(x1) = max{5, -1}
  false_A = 3
  false#_A = 3
  0_A = 1
  0#_A = 4
  s_A(x1) = max{9, 1 + x1}
  s#_A(x1) = max{2, 0}

precedence:

  cond = s > gr = p > 0 > true = false > and