YES
Time: 0.045

Problem:
 Equations:
  fAC(fAC(x3,x4),x5) -> fAC(x3,fAC(x4,x5))
  fAC(x3,x4) -> fAC(x4,x3)
  fAC(x3,fAC(x4,x5)) -> fAC(fAC(x3,x4),x5)
  fAC(x4,x3) -> fAC(x3,x4)
 TRS:
  g(fAC(x,y)) -> fAC(g(x),g(y))
  fAC(a(),g(g(a()))) -> fAC(g(a()),g(a()))

Proof:
 AC-KBO Processor:
  precedence:
   g > a ~ fAC
   weight function:
    [a] = 8,
    
    [g](x0) = x0,
    
    [fAC](x0, x1) = x0 + x1 + 2
   problem:
    Equations:
     fAC(fAC(x3,x4),x5) -> fAC(x3,fAC(x4,x5))
     fAC(x3,x4) -> fAC(x4,x3)
     fAC(x3,fAC(x4,x5)) -> fAC(fAC(x3,x4),x5)
     fAC(x4,x3) -> fAC(x3,x4)
    TRS:
     
   Qed