YES

TRS:

  f(f(x)) -> f(c(f(x)))
  f(f(x)) -> f(d(f(x)))
  g(c(x)) -> x
  g(d(x)) -> x
  g(c(h(0()))) -> g(d(1()))
  g(c(1())) -> g(d(h(0())))
  g(h(x)) -> g(x)

max/plus interpretations on N:

  f_A(x1) = max{14, 30}
  f#_A(x1) = max{0, -7 + x1}
  c_A(x1) = max{6, -15 + x1}
  c#_A(x1) = max{3, 6}
  d_A(x1) = max{8, -23 + x1}
  d#_A(x1) = max{1, -1}
  g_A(x1) = max{31, 23 + x1}
  g#_A(x1) = max{6, -3 + x1}
  h_A(x1) = max{14, 10 + x1}
  h#_A(x1) = max{2, 2}
  0_A = 6
  0#_A = 8
  1_A = 30
  1#_A = 7

precedence:

  0 > f = 1 > c > h > g > d