YES

TRS:

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

precedence:

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