YES
Time: 0.082

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(x),x)),x) -> fAC(h(x),fAC(x,x))
  fAC(h(x),g(x)) -> fAC(g(h(x)),x)
  fAC(g(h(x)),fAC(x,fAC(x,y))) -> fAC(g(fAC(h(x),y)),x)
  fAC(g(g(x)),x) -> fAC(g(x),g(x))

Proof:
 AC-KBO Processor:
  precedence:
   h ~ fAC > g
   weight function:
    [g](x0) = x0 + 1,
    
    [h](x0) = x0 + 4,
    
    [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