YES
Time: 0.002567
TRS:
 {f(x, a()) -> x,
  f(x, g y) -> f(g x, y)}
 DP:
  DP:
   {f#(x, g y) -> f#(g x, y)}
  TRS:
  {f(x, a()) -> x,
   f(x, g y) -> f(g x, y)}
  EDG:
   {(f#(x, g y) -> f#(g x, y), f#(x, g y) -> f#(g x, y))}
   STATUS:
    arrows: 0.000000
    SCCS (1):
     Scc:
      {f#(x, g y) -> f#(g x, y)}
     
     SCC (1):
      Strict:
       {f#(x, g y) -> f#(g x, y)}
      Weak:
      {f(x, a()) -> x,
       f(x, g y) -> f(g x, y)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [f](x0, x1) = x0,
        
        [g](x0) = x0 + 1,
        
        [a] = 0,
        
        [f#](x0, x1) = x0
       Strict:
        f#(x, g y) -> f#(g x, y)
        1 + 0x + 1y >= 0 + 0x + 1y
       Weak:
        f(x, g y) -> f(g x, y)
        0 + 1x + 0y >= 1 + 1x + 0y
        f(x, a()) -> x
        0 + 1x >= 1x
      Qed