YES
Time: 0.796

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:
 DP Processor:
  Equations#:
   f{AC,#}(fAC(x2,x3),x4) -> f{AC,#}(x2,fAC(x3,x4))
   f{AC,#}(x2,x3) -> f{AC,#}(x3,x2)
   f{AC,#}(x2,fAC(x3,x4)) -> f{AC,#}(fAC(x2,x3),x4)
   f{AC,#}(x3,x2) -> f{AC,#}(x2,x3)
  DPs:
   f{AC,#}(g(fAC(h(x),x)),x) -> f{AC,#}(x,x)
   f{AC,#}(g(fAC(h(x),x)),x) -> f{AC,#}(h(x),fAC(x,x))
   f{AC,#}(h(x),g(x)) -> f{AC,#}(g(h(x)),x)
   f{AC,#}(g(h(x)),fAC(x,fAC(x,y))) -> f{AC,#}(h(x),y)
   f{AC,#}(g(h(x)),fAC(x,fAC(x,y))) -> f{AC,#}(g(fAC(h(x),y)),x)
   f{AC,#}(g(g(x)),x) -> f{AC,#}(g(x),g(x))
   f{AC,#}(x5,fAC(g(fAC(h(x),x)),x)) -> f{AC,#}(x,x)
   f{AC,#}(x5,fAC(g(fAC(h(x),x)),x)) -> f{AC,#}(h(x),fAC(x,x))
   f{AC,#}(x5,fAC(g(fAC(h(x),x)),x)) -> f{AC,#}(x5,fAC(h(x),fAC(x,x)))
   f{AC,#}(x6,fAC(h(x),g(x))) -> f{AC,#}(g(h(x)),x)
   f{AC,#}(x6,fAC(h(x),g(x))) -> f{AC,#}(x6,fAC(g(h(x)),x))
   f{AC,#}(x7,fAC(g(h(x)),fAC(x,fAC(x,y)))) -> f{AC,#}(h(x),y)
   f{AC,#}(x7,fAC(g(h(x)),fAC(x,fAC(x,y)))) -> f{AC,#}(g(fAC(h(x),y)),x)
   f{AC,#}(x7,fAC(g(h(x)),fAC(x,fAC(x,y)))) -> f{AC,#}(x7,fAC(g(fAC(h(x),y)),x))
   f{AC,#}(x8,fAC(g(g(x)),x)) -> f{AC,#}(g(x),g(x))
   f{AC,#}(x8,fAC(g(g(x)),x)) -> f{AC,#}(x8,fAC(g(x),g(x)))
  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))
  S:
   f{AC,#}(fAC(x9,x10),x11) -> f{AC,#}(x9,x10)
   f{AC,#}(x9,fAC(x10,x11)) -> f{AC,#}(x10,x11)
  AC-EDG Processor:
   Equations#:
    f{AC,#}(fAC(x2,x3),x4) -> f{AC,#}(x2,fAC(x3,x4))
    f{AC,#}(x2,x3) -> f{AC,#}(x3,x2)
    f{AC,#}(x2,fAC(x3,x4)) -> f{AC,#}(fAC(x2,x3),x4)
    f{AC,#}(x3,x2) -> f{AC,#}(x2,x3)
   DPs:
    f{AC,#}(g(fAC(h(x),x)),x) -> f{AC,#}(x,x)
    f{AC,#}(g(fAC(h(x),x)),x) -> f{AC,#}(h(x),fAC(x,x))
    f{AC,#}(h(x),g(x)) -> f{AC,#}(g(h(x)),x)
    f{AC,#}(g(h(x)),fAC(x,fAC(x,y))) -> f{AC,#}(h(x),y)
    f{AC,#}(g(h(x)),fAC(x,fAC(x,y))) -> f{AC,#}(g(fAC(h(x),y)),x)
    f{AC,#}(g(g(x)),x) -> f{AC,#}(g(x),g(x))
    f{AC,#}(x5,fAC(g(fAC(h(x),x)),x)) -> f{AC,#}(x,x)
    f{AC,#}(x5,fAC(g(fAC(h(x),x)),x)) -> f{AC,#}(h(x),fAC(x,x))
    f{AC,#}(x5,fAC(g(fAC(h(x),x)),x)) -> f{AC,#}(x5,fAC(h(x),fAC(x,x)))
    f{AC,#}(x6,fAC(h(x),g(x))) -> f{AC,#}(g(h(x)),x)
    f{AC,#}(x6,fAC(h(x),g(x))) -> f{AC,#}(x6,fAC(g(h(x)),x))
    f{AC,#}(x7,fAC(g(h(x)),fAC(x,fAC(x,y)))) -> f{AC,#}(h(x),y)
    f{AC,#}(x7,fAC(g(h(x)),fAC(x,fAC(x,y)))) -> f{AC,#}(g(fAC(h(x),y)),x)
    f{AC,#}(x7,fAC(g(h(x)),fAC(x,fAC(x,y)))) -> f{AC,#}(x7,fAC(g(fAC(h(x),y)),x))
    f{AC,#}(x8,fAC(g(g(x)),x)) -> f{AC,#}(g(x),g(x))
    f{AC,#}(x8,fAC(g(g(x)),x)) -> f{AC,#}(x8,fAC(g(x),g(x)))
   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))
   S:
    f{AC,#}(fAC(x9,x10),x11) -> f{AC,#}(x9,x10)
    f{AC,#}(x9,fAC(x10,x11)) -> f{AC,#}(x10,x11)
   AC-DP unlabeling:
    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)
    DPs:
     fAC(g(fAC(h(x),x)),x) -> fAC(x,x)
     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(h(x),y)
     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))
     fAC(x5,fAC(g(fAC(h(x),x)),x)) -> fAC(x,x)
     fAC(x5,fAC(g(fAC(h(x),x)),x)) -> fAC(h(x),fAC(x,x))
     fAC(x5,fAC(g(fAC(h(x),x)),x)) -> fAC(x5,fAC(h(x),fAC(x,x)))
     fAC(x6,fAC(h(x),g(x))) -> fAC(g(h(x)),x)
     fAC(x6,fAC(h(x),g(x))) -> fAC(x6,fAC(g(h(x)),x))
     fAC(x7,fAC(g(h(x)),fAC(x,fAC(x,y)))) -> fAC(h(x),y)
     fAC(x7,fAC(g(h(x)),fAC(x,fAC(x,y)))) -> fAC(g(fAC(h(x),y)),x)
     fAC(x7,fAC(g(h(x)),fAC(x,fAC(x,y)))) -> fAC(x7,fAC(g(fAC(h(x),y)),x))
     fAC(x8,fAC(g(g(x)),x)) -> fAC(g(x),g(x))
     fAC(x8,fAC(g(g(x)),x)) -> fAC(x8,fAC(g(x),g(x)))
    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))
    S:
     fAC(fAC(x9,x10),x11) -> fAC(x9,x10)
     fAC(x9,fAC(x10,x11)) -> fAC(x10,x11)
    AC-KBO Processor:
     argument filtering:
      pi(fAC) = [0,1]
      pi(h) = []
      pi(g) = [0]
     precedence:
      h ~ fAC > g
      weight function:
       w0 = 1
       w(h) = 4
       w(g) = w(fAC) = 2
       usable rules:
        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))
       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)
        DPs:
         
        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))
        S:
         fAC(fAC(x9,x10),x11) -> fAC(x9,x10)
         fAC(x9,fAC(x10,x11)) -> fAC(x10,x11)
       Qed