YES
Time: 0.016

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:
   i > g > fAC > one
   weight function:
    [g](x0) = 6x0 + 15,
    
    [i](x0) = x0 + 5,
    
    [one] = 8,
    
    [fAC](x0, x1) = x0 + x1 + 3
   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