YES
Time: 0.050

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(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 > s ~ 0 ~ fAC
   weight function:
    [s](x0) = 12x0 + 12,
    
    [g](x0, x1) = 9x0 + 12x1,
    
    [0] = 4,
    
    [fAC](x0, x1) = x0 + x1 + 6
   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