MAYBE
Time: 7.813

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(a()),a())),a()) -> fAC(h(a()),fAC(a(),a()))
  fAC(h(a()),g(a())) -> fAC(g(h(a())),a())
  fAC(g(h(a())),fAC(fAC(a(),a()),a())) -> fAC(g(fAC(h(a()),a())),a())
  fAC(h(a()),a()) -> fAC(h(a()),b())
  fAC(i(x,y),fAC(a(),y)) -> fAC(g(i(x,y)),y)

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(a()),a())),a()) -> f{AC,#}(a(),a())
   f{AC,#}(g(fAC(h(a()),a())),a()) -> f{AC,#}(h(a()),fAC(a(),a()))
   f{AC,#}(h(a()),g(a())) -> f{AC,#}(g(h(a())),a())
   f{AC,#}(g(h(a())),fAC(fAC(a(),a()),a())) -> f{AC,#}(h(a()),a())
   f{AC,#}(g(h(a())),fAC(fAC(a(),a()),a())) -> f{AC,#}(g(fAC(h(a()),a())),a())
   f{AC,#}(h(a()),a()) -> f{AC,#}(h(a()),b())
   f{AC,#}(i(x,y),fAC(a(),y)) -> f{AC,#}(g(i(x,y)),y)
   f{AC,#}(x5,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(a(),a())
   f{AC,#}(x5,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(h(a()),fAC(a(),a()))
   f{AC,#}(x5,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(x5,fAC(h(a()),fAC(a(),a())))
   f{AC,#}(x6,fAC(h(a()),g(a()))) -> f{AC,#}(g(h(a())),a())
   f{AC,#}(x6,fAC(h(a()),g(a()))) -> f{AC,#}(x6,fAC(g(h(a())),a()))
   f{AC,#}(x7,fAC(g(h(a())),fAC(fAC(a(),a()),a()))) -> f{AC,#}(h(a()),a())
   f{AC,#}(x7,fAC(g(h(a())),fAC(fAC(a(),a()),a()))) -> f{AC,#}(g(fAC(h(a()),a())),a())
   f{AC,#}(x7,fAC(g(h(a())),fAC(fAC(a(),a()),a()))) -> f{AC,#}(x7,fAC(g(fAC(h(a()),a())),a()))
   f{AC,#}(x8,fAC(h(a()),a())) -> f{AC,#}(h(a()),b())
   f{AC,#}(x8,fAC(h(a()),a())) -> f{AC,#}(x8,fAC(h(a()),b()))
   f{AC,#}(x9,fAC(i(x,y),fAC(a(),y))) -> f{AC,#}(g(i(x,y)),y)
   f{AC,#}(x9,fAC(i(x,y),fAC(a(),y))) -> f{AC,#}(x9,fAC(g(i(x,y)),y))
  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(a()),a())),a()) -> fAC(h(a()),fAC(a(),a()))
   fAC(h(a()),g(a())) -> fAC(g(h(a())),a())
   fAC(g(h(a())),fAC(fAC(a(),a()),a())) -> fAC(g(fAC(h(a()),a())),a())
   fAC(h(a()),a()) -> fAC(h(a()),b())
   fAC(i(x,y),fAC(a(),y)) -> fAC(g(i(x,y)),y)
  S:
   f{AC,#}(fAC(x10,x11),x12) -> f{AC,#}(x10,x11)
   f{AC,#}(x10,fAC(x11,x12)) -> f{AC,#}(x11,x12)
  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(a()),a())),a()) -> f{AC,#}(a(),a())
    f{AC,#}(g(fAC(h(a()),a())),a()) -> f{AC,#}(h(a()),fAC(a(),a()))
    f{AC,#}(h(a()),g(a())) -> f{AC,#}(g(h(a())),a())
    f{AC,#}(g(h(a())),fAC(fAC(a(),a()),a())) -> f{AC,#}(h(a()),a())
    f{AC,#}(g(h(a())),fAC(fAC(a(),a()),a())) -> f{AC,#}(g(fAC(h(a()),a())),a())
    f{AC,#}(h(a()),a()) -> f{AC,#}(h(a()),b())
    f{AC,#}(i(x,y),fAC(a(),y)) -> f{AC,#}(g(i(x,y)),y)
    f{AC,#}(x5,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(a(),a())
    f{AC,#}(x5,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(h(a()),fAC(a(),a()))
    f{AC,#}(x5,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(x5,fAC(h(a()),fAC(a(),a())))
    f{AC,#}(x6,fAC(h(a()),g(a()))) -> f{AC,#}(g(h(a())),a())
    f{AC,#}(x6,fAC(h(a()),g(a()))) -> f{AC,#}(x6,fAC(g(h(a())),a()))
    f{AC,#}(x7,fAC(g(h(a())),fAC(fAC(a(),a()),a()))) -> f{AC,#}(h(a()),a())
    f{AC,#}(x7,fAC(g(h(a())),fAC(fAC(a(),a()),a()))) -> f{AC,#}(g(fAC(h(a()),a())),a())
    f{AC,#}(x7,fAC(g(h(a())),fAC(fAC(a(),a()),a()))) -> f{AC,#}(x7,fAC(g(fAC(h(a()),a())),a()))
    f{AC,#}(x8,fAC(h(a()),a())) -> f{AC,#}(h(a()),b())
    f{AC,#}(x8,fAC(h(a()),a())) -> f{AC,#}(x8,fAC(h(a()),b()))
    f{AC,#}(x9,fAC(i(x,y),fAC(a(),y))) -> f{AC,#}(g(i(x,y)),y)
    f{AC,#}(x9,fAC(i(x,y),fAC(a(),y))) -> f{AC,#}(x9,fAC(g(i(x,y)),y))
   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(a()),a())),a()) -> fAC(h(a()),fAC(a(),a()))
    fAC(h(a()),g(a())) -> fAC(g(h(a())),a())
    fAC(g(h(a())),fAC(fAC(a(),a()),a())) -> fAC(g(fAC(h(a()),a())),a())
    fAC(h(a()),a()) -> fAC(h(a()),b())
    fAC(i(x,y),fAC(a(),y)) -> fAC(g(i(x,y)),y)
   S:
    f{AC,#}(fAC(x10,x11),x12) -> f{AC,#}(x10,x11)
    f{AC,#}(x10,fAC(x11,x12)) -> f{AC,#}(x11,x12)
   Open