YES
TRS:
 {     f(f(x)) -> f(c(f(x))),
       f(f(x)) -> f(d(f(x))),
       g(c(x)) -> x,
     g(c(1())) -> g(d(h(0()))),
  g(c(h(0()))) -> g(d(1())),
       g(d(x)) -> x,
       g(h(x)) -> g(x)}
 DP:
  Strict:
   {     f#(f(x)) -> f#(c(f(x))),
         f#(f(x)) -> f#(d(f(x))),
       g#(c(1())) -> g#(d(h(0()))),
    g#(c(h(0()))) -> g#(d(1())),
         g#(h(x)) -> g#(x)}
  Weak:
  {     f(f(x)) -> f(c(f(x))),
        f(f(x)) -> f(d(f(x))),
        g(c(x)) -> x,
      g(c(1())) -> g(d(h(0()))),
   g(c(h(0()))) -> g(d(1())),
        g(d(x)) -> x,
        g(h(x)) -> g(x)}
  EDG:
   {(g#(h(x)) -> g#(x), g#(c(1())) -> g#(d(h(0()))))
    (g#(h(x)) -> g#(x), g#(c(h(0()))) -> g#(d(1())))
    (g#(h(x)) -> g#(x), g#(h(x)) -> g#(x))}
   SCCS:
    Scc:
     {g#(h(x)) -> g#(x)}
    SCC:
     Strict:
      {g#(h(x)) -> g#(x)}
     Weak:
     {     f(f(x)) -> f(c(f(x))),
           f(f(x)) -> f(d(f(x))),
           g(c(x)) -> x,
         g(c(1())) -> g(d(h(0()))),
      g(c(h(0()))) -> g(d(1())),
           g(d(x)) -> x,
           g(h(x)) -> g(x)}
     SPSC:
      Simple Projection:
       pi(g#) = 0
      Strict:
       {}
      Qed