YES
Time: 0.003273
TRS:
 {      g a() -> b(),
          a() -> g c(),
  f(g X, b()) -> f(a(), X)}
 DP:
  DP:
   {        a#() -> g# c(),
    f#(g X, b()) -> a#(),
    f#(g X, b()) -> f#(a(), X)}
  TRS:
  {      g a() -> b(),
           a() -> g c(),
   f(g X, b()) -> f(a(), X)}
  EDG:
   {(f#(g X, b()) -> a#(), a#() -> g# c())
    (f#(g X, b()) -> f#(a(), X), f#(g X, b()) -> a#())
    (f#(g X, b()) -> f#(a(), X), f#(g X, b()) -> f#(a(), X))}
   SCCS (1):
    Scc:
     {f#(g X, b()) -> f#(a(), X)}
    SCC (1):
     Strict:
      {f#(g X, b()) -> f#(a(), X)}
     Weak:
     {      g a() -> b(),
              a() -> g c(),
      f(g X, b()) -> f(a(), X)}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [f](x0, x1) = 0,
       
       [g](x0) = x0 + 1,
       
       [c] = 0,
       
       [a] = 1,
       
       [b] = 1,
       
       [f#](x0, x1) = x0 + x1
      Strict:
       f#(g X, b()) -> f#(a(), X)
       2 + 1X >= 1 + 1X
      Weak:
       
     Qed