MAYBE
Time: 0.588

Problem:
 Equations:
  plusAC(plusAC(x4,x5),x6) -> plusAC(x4,plusAC(x5,x6))
  plusAC(x4,x5) -> plusAC(x5,x4)
  plusAC(x4,plusAC(x5,x6)) -> plusAC(plusAC(x4,x5),x6)
  plusAC(x5,x4) -> plusAC(x4,x5)
 TRS:
  app(nil(),k) -> k
  app(l,nil()) -> l
  app(cons(x,l),k) -> cons(x,app(l,k))
  sum(cons(x,nil())) -> cons(x,nil())
  sum(cons(x,cons(y,l))) -> sum(cons(plusAC(x,y),l))
  sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
  sum(cons(0(),cons(plusAC(x,y),l))) -> pred(sum(cons(s(x),cons(y,l))))
  plusAC(0(),y) -> y
  plusAC(s(x),y) -> s(plusAC(x,y))
  pred(cons(s(x),nil())) -> cons(x,nil())

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x4,x5),x6) -> plus{AC,#}(x4,plusAC(x5,x6))
   plus{AC,#}(x4,x5) -> plus{AC,#}(x5,x4)
   plus{AC,#}(x4,plusAC(x5,x6)) -> plus{AC,#}(plusAC(x4,x5),x6)
   plus{AC,#}(x5,x4) -> plus{AC,#}(x4,x5)
  DPs:
   app#(cons(x,l),k) -> app#(l,k)
   sum#(cons(x,cons(y,l))) -> plus{AC,#}(x,y)
   sum#(cons(x,cons(y,l))) -> sum#(cons(plusAC(x,y),l))
   sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
   sum#(app(l,cons(x,cons(y,k)))) -> app#(l,sum(cons(x,cons(y,k))))
   sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
   sum#(cons(0(),cons(plusAC(x,y),l))) -> sum#(cons(s(x),cons(y,l)))
   sum#(cons(0(),cons(plusAC(x,y),l))) -> pred#(sum(cons(s(x),cons(y,l))))
   plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
   plus{AC,#}(x7,plusAC(0(),y)) -> plus{AC,#}(x7,y)
   plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x8,s(plusAC(x,y)))
  Equations:
   plusAC(plusAC(x4,x5),x6) -> plusAC(x4,plusAC(x5,x6))
   plusAC(x4,x5) -> plusAC(x5,x4)
   plusAC(x4,plusAC(x5,x6)) -> plusAC(plusAC(x4,x5),x6)
   plusAC(x5,x4) -> plusAC(x4,x5)
  TRS:
   app(nil(),k) -> k
   app(l,nil()) -> l
   app(cons(x,l),k) -> cons(x,app(l,k))
   sum(cons(x,nil())) -> cons(x,nil())
   sum(cons(x,cons(y,l))) -> sum(cons(plusAC(x,y),l))
   sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
   sum(cons(0(),cons(plusAC(x,y),l))) -> pred(sum(cons(s(x),cons(y,l))))
   plusAC(0(),y) -> y
   plusAC(s(x),y) -> s(plusAC(x,y))
   pred(cons(s(x),nil())) -> cons(x,nil())
  S:
   plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
   plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x4,x5),x6) -> plus{AC,#}(x4,plusAC(x5,x6))
    plus{AC,#}(x4,x5) -> plus{AC,#}(x5,x4)
    plus{AC,#}(x4,plusAC(x5,x6)) -> plus{AC,#}(plusAC(x4,x5),x6)
    plus{AC,#}(x5,x4) -> plus{AC,#}(x4,x5)
   DPs:
    app#(cons(x,l),k) -> app#(l,k)
    sum#(cons(x,cons(y,l))) -> plus{AC,#}(x,y)
    sum#(cons(x,cons(y,l))) -> sum#(cons(plusAC(x,y),l))
    sum#(app(l,cons(x,cons(y,k)))) -> sum#(cons(x,cons(y,k)))
    sum#(app(l,cons(x,cons(y,k)))) -> app#(l,sum(cons(x,cons(y,k))))
    sum#(app(l,cons(x,cons(y,k)))) -> sum#(app(l,sum(cons(x,cons(y,k)))))
    sum#(cons(0(),cons(plusAC(x,y),l))) -> sum#(cons(s(x),cons(y,l)))
    sum#(cons(0(),cons(plusAC(x,y),l))) -> pred#(sum(cons(s(x),cons(y,l))))
    plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
    plus{AC,#}(x7,plusAC(0(),y)) -> plus{AC,#}(x7,y)
    plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x8,plusAC(s(x),y)) -> plus{AC,#}(x8,s(plusAC(x,y)))
   Equations:
    plusAC(plusAC(x4,x5),x6) -> plusAC(x4,plusAC(x5,x6))
    plusAC(x4,x5) -> plusAC(x5,x4)
    plusAC(x4,plusAC(x5,x6)) -> plusAC(plusAC(x4,x5),x6)
    plusAC(x5,x4) -> plusAC(x4,x5)
   TRS:
    app(nil(),k) -> k
    app(l,nil()) -> l
    app(cons(x,l),k) -> cons(x,app(l,k))
    sum(cons(x,nil())) -> cons(x,nil())
    sum(cons(x,cons(y,l))) -> sum(cons(plusAC(x,y),l))
    sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
    sum(cons(0(),cons(plusAC(x,y),l))) -> pred(sum(cons(s(x),cons(y,l))))
    plusAC(0(),y) -> y
    plusAC(s(x),y) -> s(plusAC(x,y))
    pred(cons(s(x),nil())) -> cons(x,nil())
   S:
    plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
    plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
   Open