YES
Time: 0.118

Problem:
 Equations:
  
 TRS:
  g(0(),fAC(x,x)) -> x
  g(x,s(y)) -> g(fAC(x,y),0())
  g(s(x),y) -> g(fAC(x,y),0())
  g(fAC(x,y),0()) -> fAC(g(x,0()),g(y,0()))

Proof:
 AC-KBO Processor:
  precedence:
   g > fAC > s > 0
   weight function:
    [s](x0) = 9x0 + 6,
    
    [g](x0, x1) = 4x0 + 5x1 + 1,
    
    [0] = 1,
    
    [fAC](x0, x1) = x0 + x1 + 4
   problem:
    Equations:
     
    TRS:
     
   Qed