YES
Time: 0.177

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(g(fAC(h(a()),a())),a()) -> fAC(h(a()),fAC(a(),a()))
  fAC(h(a()),g(a())) -> fAC(g(h(a())),a())
  fAC(g(h(a())),fAC(fAC(a(),a()),a())) -> fAC(g(fAC(h(a()),a())),a())
  fAC(h(a()),a()) -> fAC(h(a()),b())
  fAC(i(x,y),fAC(a(),y)) -> fAC(g(i(x,y)),y)

Proof:
 AC-KBO Processor:
  precedence:
   h > i ~ fAC > a > b ~ g
   weight function:
    [i](x0, x1) = 2x0 + 8x1 + 9,
    
    [b] = 1,
    
    [g](x0) = x0 + 1,
    
    [h](x0) = x0,
    
    [a] = 1,
    
    [fAC](x0, x1) = x0 + x1
   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