YES
TRS:
 {      g(a()) -> b(),
           a() -> g(c()),
  f(g(X), b()) -> f(a(), X)}
 DP:
  Strict:
   {         a#() -> g#(c()),
    f#(g(X), b()) -> a#(),
    f#(g(X), b()) -> f#(a(), X)}
  Weak:
  {      g(a()) -> b(),
            a() -> g(c()),
   f(g(X), b()) -> f(a(), X)}
  EDG:
   {(f#(g(X), b()) -> f#(a(), X), f#(g(X), b()) -> f#(a(), X))
    (f#(g(X), b()) -> f#(a(), X), f#(g(X), b()) -> a#())
    (f#(g(X), b()) -> a#(), a#() -> g#(c()))}
   SCCS:
    Scc:
     {f#(g(X), b()) -> f#(a(), X)}
    SCC:
     Strict:
      {f#(g(X), b()) -> f#(a(), X)}
     Weak:
     {      g(a()) -> b(),
               a() -> g(c()),
      f(g(X), b()) -> f(a(), X)}
     POLY:
      Argument Filtering:
       pi(f#) = [0,1], pi(f) = [], pi(b) = [], pi(a) = [], pi(c) = [], pi(g) = [0]
      Usable Rules:
       {}
      Interpretation:
       [f#](x0, x1) = x0 + x1,
       [g](x0) = x0 + 1,
       [b] = 1,
       [a] = 1
      Strict:
       {}
      Weak:
       {      g(a()) -> b(),
                 a() -> g(c()),
        f(g(X), b()) -> f(a(), X)}
      Qed