YES
Time: 0.132

Problem:
 Equations:
  fAC(fAC(x0,x1),x2) -> fAC(x0,fAC(x1,x2))
  fAC(x0,x1) -> fAC(x1,x0)
  fAC(x0,fAC(x1,x2)) -> fAC(fAC(x0,x1),x2)
  fAC(x1,x0) -> fAC(x0,x1)
 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(b(),fAC(b(),b()))) -> fAC(g(fAC(h(a()),a())),a())
  fAC(h(a()),a()) -> fAC(h(a()),b())

Proof:
 AC-KBO Processor:
  precedence:
   h > fAC > a > b ~ g
   weight function:
    [b] = 1,
    
    [g](x0) = x0 + 1,
    
    [h](x0) = 8x0 + 12,
    
    [a] = 1,
    
    [fAC](x0, x1) = x0 + x1
   problem:
    Equations:
     fAC(fAC(x0,x1),x2) -> fAC(x0,fAC(x1,x2))
     fAC(x0,x1) -> fAC(x1,x0)
     fAC(x0,fAC(x1,x2)) -> fAC(fAC(x0,x1),x2)
     fAC(x1,x0) -> fAC(x0,x1)
    TRS:
     
   Qed