YES
Time: 0.011

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 > fAC > a
   weight function:
    w0 = 8
    w(a) = 8
    w(g) = w(fAC) = 0
   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