YES
Time: 0.022

Problem:
 Equations:
  
 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-RPO Processor:
  precedence:
   h > fAC > g
  status:
   
  problem:
   Equations:
    
   TRS:
    
  Qed