MAYBE
Time: 2.143

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)
   Open