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(0())),
  g(c(0())) -> g(d(1())),
    g(d(x)) -> x}
 DP:
  Strict:
   {  f#(f(x)) -> f#(c(f(x))),
      f#(f(x)) -> f#(d(f(x))),
    g#(c(1())) -> g#(d(0())),
    g#(c(0())) -> g#(d(1()))}
  Weak:
  {  f(f(x)) -> f(c(f(x))),
     f(f(x)) -> f(d(f(x))),
     g(c(x)) -> x,
   g(c(1())) -> g(d(0())),
   g(c(0())) -> g(d(1())),
     g(d(x)) -> x}
  EDG:
   {}
   SCCS:
    
    Qed