MAYBE
Time: 0.244

Problem:
 Equations:
  plusAC(plusAC(x5,x6),x7) -> plusAC(x5,plusAC(x6,x7))
  plusAC(x5,x6) -> plusAC(x6,x5)
  plusAC(x5,plusAC(x6,x7)) -> plusAC(plusAC(x5,x6),x7)
  plusAC(x6,x5) -> plusAC(x5,x6)
 TRS:
  minus(x,0()) -> x
  minus(s(x),s(y)) -> minus(x,y)
  minus(minus(x,y),z) -> minus(x,plusAC(y,z))
  quot(0(),s(y)) -> 0()
  quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
  plusAC(0(),y) -> y
  plusAC(s(x),y) -> s(plusAC(x,y))
  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)))))

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x5,x6),x7) -> plus{AC,#}(x5,plusAC(x6,x7))
   plus{AC,#}(x5,x6) -> plus{AC,#}(x6,x5)
   plus{AC,#}(x5,plusAC(x6,x7)) -> plus{AC,#}(plusAC(x5,x6),x7)
   plus{AC,#}(x6,x5) -> plus{AC,#}(x5,x6)
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   minus#(minus(x,y),z) -> plus{AC,#}(y,z)
   minus#(minus(x,y),z) -> minus#(x,plusAC(y,z))
   quot#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
   plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
   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)))))
   plus{AC,#}(x8,plusAC(0(),y)) -> plus{AC,#}(x8,y)
   plus{AC,#}(x9,plusAC(s(x),y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x9,plusAC(s(x),y)) -> plus{AC,#}(x9,s(plusAC(x,y)))
  Equations:
   plusAC(plusAC(x5,x6),x7) -> plusAC(x5,plusAC(x6,x7))
   plusAC(x5,x6) -> plusAC(x6,x5)
   plusAC(x5,plusAC(x6,x7)) -> plusAC(plusAC(x5,x6),x7)
   plusAC(x6,x5) -> plusAC(x5,x6)
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   minus(minus(x,y),z) -> minus(x,plusAC(y,z))
   quot(0(),s(y)) -> 0()
   quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
   plusAC(0(),y) -> y
   plusAC(s(x),y) -> s(plusAC(x,y))
   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)))))
  S:
   plus{AC,#}(plusAC(x10,x11),x12) -> plus{AC,#}(x10,x11)
   plus{AC,#}(x10,plusAC(x11,x12)) -> plus{AC,#}(x11,x12)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x5,x6),x7) -> plus{AC,#}(x5,plusAC(x6,x7))
    plus{AC,#}(x5,x6) -> plus{AC,#}(x6,x5)
    plus{AC,#}(x5,plusAC(x6,x7)) -> plus{AC,#}(plusAC(x5,x6),x7)
    plus{AC,#}(x6,x5) -> plus{AC,#}(x5,x6)
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    minus#(minus(x,y),z) -> plus{AC,#}(y,z)
    minus#(minus(x,y),z) -> minus#(x,plusAC(y,z))
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
    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)))))
    plus{AC,#}(x8,plusAC(0(),y)) -> plus{AC,#}(x8,y)
    plus{AC,#}(x9,plusAC(s(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x9,plusAC(s(x),y)) -> plus{AC,#}(x9,s(plusAC(x,y)))
   Equations:
    plusAC(plusAC(x5,x6),x7) -> plusAC(x5,plusAC(x6,x7))
    plusAC(x5,x6) -> plusAC(x6,x5)
    plusAC(x5,plusAC(x6,x7)) -> plusAC(plusAC(x5,x6),x7)
    plusAC(x6,x5) -> plusAC(x5,x6)
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    minus(minus(x,y),z) -> minus(x,plusAC(y,z))
    quot(0(),s(y)) -> 0()
    quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
    plusAC(0(),y) -> y
    plusAC(s(x),y) -> s(plusAC(x,y))
    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)))))
   S:
    plus{AC,#}(plusAC(x10,x11),x12) -> plus{AC,#}(x10,x11)
    plus{AC,#}(x10,plusAC(x11,x12)) -> plus{AC,#}(x11,x12)
   Open