MAYBE
Time: 0.059

Problem:
 Equations:
  hAC(hAC(x1,x2),x3) -> hAC(x1,hAC(x2,x3))
  hAC(x1,x2) -> hAC(x2,x1)
  hAC(x1,hAC(x2,x3)) -> hAC(hAC(x1,x2),x3)
  hAC(x2,x1) -> hAC(x1,x2)
 TRS:
  f(f(x)) -> f(g(x))
  g(x) -> hAC(f(x),f(x))

Proof:
 DP Processor:
  Equations#:
   h{AC,#}(hAC(x1,x2),x3) -> h{AC,#}(x1,hAC(x2,x3))
   h{AC,#}(x1,x2) -> h{AC,#}(x2,x1)
   h{AC,#}(x1,hAC(x2,x3)) -> h{AC,#}(hAC(x1,x2),x3)
   h{AC,#}(x2,x1) -> h{AC,#}(x1,x2)
  DPs:
   f#(f(x)) -> g#(x)
   f#(f(x)) -> f#(g(x))
   g#(x) -> f#(x)
  Equations:
   hAC(hAC(x1,x2),x3) -> hAC(x1,hAC(x2,x3))
   hAC(x1,x2) -> hAC(x2,x1)
   hAC(x1,hAC(x2,x3)) -> hAC(hAC(x1,x2),x3)
   hAC(x2,x1) -> hAC(x1,x2)
  TRS:
   f(f(x)) -> f(g(x))
   g(x) -> hAC(f(x),f(x))
  S:
   h{AC,#}(hAC(x4,x5),x6) -> h{AC,#}(x4,x5)
   h{AC,#}(x4,hAC(x5,x6)) -> h{AC,#}(x5,x6)
  AC-EDG Processor:
   Equations#:
    h{AC,#}(hAC(x1,x2),x3) -> h{AC,#}(x1,hAC(x2,x3))
    h{AC,#}(x1,x2) -> h{AC,#}(x2,x1)
    h{AC,#}(x1,hAC(x2,x3)) -> h{AC,#}(hAC(x1,x2),x3)
    h{AC,#}(x2,x1) -> h{AC,#}(x1,x2)
   DPs:
    f#(f(x)) -> g#(x)
    f#(f(x)) -> f#(g(x))
    g#(x) -> f#(x)
   Equations:
    hAC(hAC(x1,x2),x3) -> hAC(x1,hAC(x2,x3))
    hAC(x1,x2) -> hAC(x2,x1)
    hAC(x1,hAC(x2,x3)) -> hAC(hAC(x1,x2),x3)
    hAC(x2,x1) -> hAC(x1,x2)
   TRS:
    f(f(x)) -> f(g(x))
    g(x) -> hAC(f(x),f(x))
   S:
    h{AC,#}(hAC(x4,x5),x6) -> h{AC,#}(x4,x5)
    h{AC,#}(x4,hAC(x5,x6)) -> h{AC,#}(x5,x6)
   Open