YES
Time: 0.014

Problem:
 Equations:
  fAC(fAC(x2,x3),x4) -> fAC(x2,fAC(x3,x4))
  fAC(x2,x3) -> fAC(x3,x2)
  fAC(x2,fAC(x3,x4)) -> fAC(fAC(x2,x3),x4)
  fAC(x3,x2) -> fAC(x2,x3)
 TRS:
  fAC(x,one()) -> x
  fAC(i(x),x) -> one()
  g(one()) -> one()
  g(fAC(x,y)) -> fAC(g(x),g(y))

Proof:
 AC-KBO Processor:
  precedence:
   g > fAC > i ~ one
   weight function:
    w0 = 2
    w(one) = 9
    w(i) = 4
    w(fAC) = 1
    w(g) = 0
   problem:
    Equations:
     fAC(fAC(x2,x3),x4) -> fAC(x2,fAC(x3,x4))
     fAC(x2,x3) -> fAC(x3,x2)
     fAC(x2,fAC(x3,x4)) -> fAC(fAC(x2,x3),x4)
     fAC(x3,x2) -> fAC(x2,x3)
    TRS:
     
   Qed