YES

TRS:

  cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
  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) = max{0, 0, 1, -1}
  cond#_A(x1,x2,x3) = max{0, -3 + x1, 4 + x2, 2 + x3}
  true_A = 14
  true#_A = 9
  and_A(x1,x2) = max{2, 1, x2}
  and#_A(x1,x2) = max{10, 5, 7}
  gr_A(x1,x2) = max{0, 1 + x1, -1}
  gr#_A(x1,x2) = max{7, 10, 8}
  0_A = 1
  0#_A = 8
  p_A(x1) = max{1, -5 + x1}
  p#_A(x1) = max{10, 1}
  false_A = 2
  false#_A = 6
  s_A(x1) = max{1, 13 + x1}
  s#_A(x1) = max{10, 8}

precedence:

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