MAYBE
Time: 5.100

Problem:
 Equations:
  fAC(fAC(x0,x1),x2) -> fAC(x0,fAC(x1,x2))
  fAC(x0,x1) -> fAC(x1,x0)
  fAC(x0,fAC(x1,x2)) -> fAC(fAC(x0,x1),x2)
  fAC(x1,x0) -> fAC(x0,x1)
 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(b(),fAC(b(),b()))) -> fAC(g(fAC(h(a()),a())),a())
  fAC(h(a()),a()) -> fAC(h(a()),b())

Proof:
 DP Processor:
  Equations#:
   f{AC,#}(fAC(x0,x1),x2) -> f{AC,#}(x0,fAC(x1,x2))
   f{AC,#}(x0,x1) -> f{AC,#}(x1,x0)
   f{AC,#}(x0,fAC(x1,x2)) -> f{AC,#}(fAC(x0,x1),x2)
   f{AC,#}(x1,x0) -> f{AC,#}(x0,x1)
  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(b(),fAC(b(),b()))) -> f{AC,#}(h(a()),a())
   f{AC,#}(g(h(a())),fAC(b(),fAC(b(),b()))) -> f{AC,#}(g(fAC(h(a()),a())),a())
   f{AC,#}(h(a()),a()) -> f{AC,#}(h(a()),b())
   f{AC,#}(x3,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(a(),a())
   f{AC,#}(x3,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(h(a()),fAC(a(),a()))
   f{AC,#}(x3,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(x3,fAC(h(a()),fAC(a(),a())))
   f{AC,#}(x4,fAC(h(a()),g(a()))) -> f{AC,#}(g(h(a())),a())
   f{AC,#}(x4,fAC(h(a()),g(a()))) -> f{AC,#}(x4,fAC(g(h(a())),a()))
   f{AC,#}(x5,fAC(g(h(a())),fAC(b(),fAC(b(),b())))) -> f{AC,#}(h(a()),a())
   f{AC,#}(x5,fAC(g(h(a())),fAC(b(),fAC(b(),b())))) -> f{AC,#}(g(fAC(h(a()),a())),a())
   f{AC,#}(x5,fAC(g(h(a())),fAC(b(),fAC(b(),b())))) -> f{AC,#}(x5,fAC(g(fAC(h(a()),a())),a()))
   f{AC,#}(x6,fAC(h(a()),a())) -> f{AC,#}(h(a()),b())
   f{AC,#}(x6,fAC(h(a()),a())) -> f{AC,#}(x6,fAC(h(a()),b()))
  Equations:
   fAC(fAC(x0,x1),x2) -> fAC(x0,fAC(x1,x2))
   fAC(x0,x1) -> fAC(x1,x0)
   fAC(x0,fAC(x1,x2)) -> fAC(fAC(x0,x1),x2)
   fAC(x1,x0) -> fAC(x0,x1)
  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(b(),fAC(b(),b()))) -> fAC(g(fAC(h(a()),a())),a())
   fAC(h(a()),a()) -> fAC(h(a()),b())
  S:
   f{AC,#}(fAC(x7,x8),x9) -> f{AC,#}(x7,x8)
   f{AC,#}(x7,fAC(x8,x9)) -> f{AC,#}(x8,x9)
  AC-EDG Processor:
   Equations#:
    f{AC,#}(fAC(x0,x1),x2) -> f{AC,#}(x0,fAC(x1,x2))
    f{AC,#}(x0,x1) -> f{AC,#}(x1,x0)
    f{AC,#}(x0,fAC(x1,x2)) -> f{AC,#}(fAC(x0,x1),x2)
    f{AC,#}(x1,x0) -> f{AC,#}(x0,x1)
   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(b(),fAC(b(),b()))) -> f{AC,#}(h(a()),a())
    f{AC,#}(g(h(a())),fAC(b(),fAC(b(),b()))) -> f{AC,#}(g(fAC(h(a()),a())),a())
    f{AC,#}(h(a()),a()) -> f{AC,#}(h(a()),b())
    f{AC,#}(x3,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(a(),a())
    f{AC,#}(x3,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(h(a()),fAC(a(),a()))
    f{AC,#}(x3,fAC(g(fAC(h(a()),a())),a())) -> f{AC,#}(x3,fAC(h(a()),fAC(a(),a())))
    f{AC,#}(x4,fAC(h(a()),g(a()))) -> f{AC,#}(g(h(a())),a())
    f{AC,#}(x4,fAC(h(a()),g(a()))) -> f{AC,#}(x4,fAC(g(h(a())),a()))
    f{AC,#}(x5,fAC(g(h(a())),fAC(b(),fAC(b(),b())))) -> f{AC,#}(h(a()),a())
    f{AC,#}(x5,fAC(g(h(a())),fAC(b(),fAC(b(),b())))) -> f{AC,#}(g(fAC(h(a()),a())),a())
    f{AC,#}(x5,fAC(g(h(a())),fAC(b(),fAC(b(),b())))) -> f{AC,#}(x5,fAC(g(fAC(h(a()),a())),a()))
    f{AC,#}(x6,fAC(h(a()),a())) -> f{AC,#}(h(a()),b())
    f{AC,#}(x6,fAC(h(a()),a())) -> f{AC,#}(x6,fAC(h(a()),b()))
   Equations:
    fAC(fAC(x0,x1),x2) -> fAC(x0,fAC(x1,x2))
    fAC(x0,x1) -> fAC(x1,x0)
    fAC(x0,fAC(x1,x2)) -> fAC(fAC(x0,x1),x2)
    fAC(x1,x0) -> fAC(x0,x1)
   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(b(),fAC(b(),b()))) -> fAC(g(fAC(h(a()),a())),a())
    fAC(h(a()),a()) -> fAC(h(a()),b())
   S:
    f{AC,#}(fAC(x7,x8),x9) -> f{AC,#}(x7,x8)
    f{AC,#}(x7,fAC(x8,x9)) -> f{AC,#}(x8,x9)
   Open