YES
Time: 0.187

Problem:
 Equations:
  plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
  plusAC(x2,x3) -> plusAC(x3,x2)
  timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
  timesAC(x2,x3) -> timesAC(x3,x2)
  plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
  plusAC(x3,x2) -> plusAC(x2,x3)
  timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
  timesAC(x3,x2) -> timesAC(x2,x3)
 TRS:
  plusAC(x,0()) -> x
  plusAC(x,s(y)) -> s(plusAC(x,y))
  timesAC(x,0()) -> 0()
  timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
  minus(x,0()) -> x
  minus(s(x),s(y)) -> minus(x,y)
  div(0(),s(y)) -> 0()
  div(s(x),s(y)) -> s(div(minus(x,y),s(y)))

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
   plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
   times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
   times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
   plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
   plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
   times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
   times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
  DPs:
   plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
   times{AC,#}(x,s(y)) -> times{AC,#}(x,y)
   times{AC,#}(x,s(y)) -> plus{AC,#}(timesAC(x,y),x)
   minus#(s(x),s(y)) -> minus#(x,y)
   div#(s(x),s(y)) -> minus#(x,y)
   div#(s(x),s(y)) -> div#(minus(x,y),s(y))
   plus{AC,#}(x5,plusAC(x,0())) -> plus{AC,#}(x5,x)
   plus{AC,#}(x6,plusAC(x,s(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x6,plusAC(x,s(y))) -> plus{AC,#}(x6,s(plusAC(x,y)))
   times{AC,#}(x7,timesAC(x,0())) -> times{AC,#}(x7,0())
   times{AC,#}(x8,timesAC(x,s(y))) -> times{AC,#}(x,y)
   times{AC,#}(x8,timesAC(x,s(y))) -> plus{AC,#}(timesAC(x,y),x)
   times{AC,#}(x8,timesAC(x,s(y))) -> times{AC,#}(x8,plusAC(timesAC(x,y),x))
  Equations:
   plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
   plusAC(x2,x3) -> plusAC(x3,x2)
   timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
   timesAC(x2,x3) -> timesAC(x3,x2)
   plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
   plusAC(x3,x2) -> plusAC(x2,x3)
   timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
   timesAC(x3,x2) -> timesAC(x2,x3)
  TRS:
   plusAC(x,0()) -> x
   plusAC(x,s(y)) -> s(plusAC(x,y))
   timesAC(x,0()) -> 0()
   timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   div(0(),s(y)) -> 0()
   div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
  S:
   plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
   plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
   times{AC,#}(timesAC(x9,x10),x11) -> times{AC,#}(x9,x10)
   times{AC,#}(x9,timesAC(x10,x11)) -> times{AC,#}(x10,x11)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
    plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
    times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
    times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
    plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
    plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
    times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
    times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
   DPs:
    plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
    times{AC,#}(x,s(y)) -> times{AC,#}(x,y)
    times{AC,#}(x,s(y)) -> plus{AC,#}(timesAC(x,y),x)
    minus#(s(x),s(y)) -> minus#(x,y)
    div#(s(x),s(y)) -> minus#(x,y)
    div#(s(x),s(y)) -> div#(minus(x,y),s(y))
    plus{AC,#}(x5,plusAC(x,0())) -> plus{AC,#}(x5,x)
    plus{AC,#}(x6,plusAC(x,s(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x6,plusAC(x,s(y))) -> plus{AC,#}(x6,s(plusAC(x,y)))
    times{AC,#}(x7,timesAC(x,0())) -> times{AC,#}(x7,0())
    times{AC,#}(x8,timesAC(x,s(y))) -> times{AC,#}(x,y)
    times{AC,#}(x8,timesAC(x,s(y))) -> plus{AC,#}(timesAC(x,y),x)
    times{AC,#}(x8,timesAC(x,s(y))) -> times{AC,#}(x8,plusAC(timesAC(x,y),x))
   Equations:
    plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
    plusAC(x2,x3) -> plusAC(x3,x2)
    timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
    timesAC(x2,x3) -> timesAC(x3,x2)
    plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
    plusAC(x3,x2) -> plusAC(x2,x3)
    timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
    timesAC(x3,x2) -> timesAC(x2,x3)
   TRS:
    plusAC(x,0()) -> x
    plusAC(x,s(y)) -> s(plusAC(x,y))
    timesAC(x,0()) -> 0()
    timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    div(0(),s(y)) -> 0()
    div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
   S:
    plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
    plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
    times{AC,#}(timesAC(x9,x10),x11) -> times{AC,#}(x9,x10)
    times{AC,#}(x9,timesAC(x10,x11)) -> times{AC,#}(x10,x11)
   SCC Processor:
    #sccs: 4
    #rules: 10
    #arcs: 52/169
    Equations#:
     plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
     plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
     times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
     times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
     plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
     plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
     times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
     times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
    DPs:
     times{AC,#}(x8,timesAC(x,s(y))) -> times{AC,#}(x8,plusAC(timesAC(x,y),x))
     times{AC,#}(x8,timesAC(x,s(y))) -> times{AC,#}(x,y)
     times{AC,#}(x7,timesAC(x,0())) -> times{AC,#}(x7,0())
     times{AC,#}(x,s(y)) -> times{AC,#}(x,y)
    Equations:
     plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
     plusAC(x2,x3) -> plusAC(x3,x2)
     timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
     timesAC(x2,x3) -> timesAC(x3,x2)
     plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
     plusAC(x3,x2) -> plusAC(x2,x3)
     timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
     timesAC(x3,x2) -> timesAC(x2,x3)
    TRS:
     plusAC(x,0()) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     timesAC(x,0()) -> 0()
     timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     div(0(),s(y)) -> 0()
     div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
    S:
     plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
     plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
     times{AC,#}(timesAC(x9,x10),x11) -> times{AC,#}(x9,x10)
     times{AC,#}(x9,timesAC(x10,x11)) -> times{AC,#}(x10,x11)
    AC-DP unlabeling:
     Equations#:
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
     DPs:
      timesAC(x8,timesAC(x,s(y))) -> timesAC(x8,plusAC(timesAC(x,y),x))
      timesAC(x8,timesAC(x,s(y))) -> timesAC(x,y)
      timesAC(x7,timesAC(x,0())) -> timesAC(x7,0())
      timesAC(x,s(y)) -> timesAC(x,y)
     Equations:
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
     TRS:
      plusAC(x,0()) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      timesAC(x,0()) -> 0()
      timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      div(0(),s(y)) -> 0()
      div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
     S:
      plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
      plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
      timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
      timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
     Usable Rule Processor:
      Equations#:
       plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
       plusAC(x2,x3) -> plusAC(x3,x2)
       timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
       timesAC(x2,x3) -> timesAC(x3,x2)
       plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
       plusAC(x3,x2) -> plusAC(x2,x3)
       timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
       timesAC(x3,x2) -> timesAC(x2,x3)
      DPs:
       timesAC(x8,timesAC(x,s(y))) -> timesAC(x8,plusAC(timesAC(x,y),x))
       timesAC(x8,timesAC(x,s(y))) -> timesAC(x,y)
       timesAC(x7,timesAC(x,0())) -> timesAC(x7,0())
       timesAC(x,s(y)) -> timesAC(x,y)
      Equations:
       plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
       plusAC(x2,x3) -> plusAC(x3,x2)
       timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
       timesAC(x2,x3) -> timesAC(x3,x2)
       plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
       plusAC(x3,x2) -> plusAC(x2,x3)
       timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
       timesAC(x3,x2) -> timesAC(x2,x3)
      TRS:
       timesAC(x,0()) -> 0()
       timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
       plusAC(x,0()) -> x
       plusAC(x,s(y)) -> s(plusAC(x,y))
      S:
       plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
       plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
       timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
       timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(timesAC) = [0,1]
        pi(0) = []
        pi(s) = [0]
       precedence:
        timesAC > plusAC > s > 0
       status:
        
       problem:
        Equations#:
         plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
         plusAC(x2,x3) -> plusAC(x3,x2)
         timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
         timesAC(x2,x3) -> timesAC(x3,x2)
         plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
         plusAC(x3,x2) -> plusAC(x2,x3)
         timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
         timesAC(x3,x2) -> timesAC(x2,x3)
        DPs:
         
        Equations:
         plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
         plusAC(x2,x3) -> plusAC(x3,x2)
         timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
         timesAC(x2,x3) -> timesAC(x3,x2)
         plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
         plusAC(x3,x2) -> plusAC(x2,x3)
         timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
         timesAC(x3,x2) -> timesAC(x2,x3)
        TRS:
         timesAC(x,0()) -> 0()
         timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
         plusAC(x,0()) -> x
         plusAC(x,s(y)) -> s(plusAC(x,y))
        S:
         plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
         plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
         timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
         timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
       Qed
    
    Equations#:
     plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
     plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
     times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
     times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
     plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
     plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
     times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
     times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
    DPs:
     plus{AC,#}(x6,plusAC(x,s(y))) -> plus{AC,#}(x6,s(plusAC(x,y)))
     plus{AC,#}(x6,plusAC(x,s(y))) -> plus{AC,#}(x,y)
     plus{AC,#}(x5,plusAC(x,0())) -> plus{AC,#}(x5,x)
     plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
    Equations:
     plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
     plusAC(x2,x3) -> plusAC(x3,x2)
     timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
     timesAC(x2,x3) -> timesAC(x3,x2)
     plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
     plusAC(x3,x2) -> plusAC(x2,x3)
     timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
     timesAC(x3,x2) -> timesAC(x2,x3)
    TRS:
     plusAC(x,0()) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     timesAC(x,0()) -> 0()
     timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     div(0(),s(y)) -> 0()
     div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
    S:
     plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
     plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
     times{AC,#}(timesAC(x9,x10),x11) -> times{AC,#}(x9,x10)
     times{AC,#}(x9,timesAC(x10,x11)) -> times{AC,#}(x10,x11)
    AC-DP unlabeling:
     Equations#:
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
     DPs:
      plusAC(x6,plusAC(x,s(y))) -> plusAC(x6,s(plusAC(x,y)))
      plusAC(x6,plusAC(x,s(y))) -> plusAC(x,y)
      plusAC(x5,plusAC(x,0())) -> plusAC(x5,x)
      plusAC(x,s(y)) -> plusAC(x,y)
     Equations:
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
     TRS:
      plusAC(x,0()) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      timesAC(x,0()) -> 0()
      timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      div(0(),s(y)) -> 0()
      div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
     S:
      plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
      plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
      timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
      timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
     Usable Rule Processor:
      Equations#:
       plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
       plusAC(x2,x3) -> plusAC(x3,x2)
       timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
       timesAC(x2,x3) -> timesAC(x3,x2)
       plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
       plusAC(x3,x2) -> plusAC(x2,x3)
       timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
       timesAC(x3,x2) -> timesAC(x2,x3)
      DPs:
       plusAC(x6,plusAC(x,s(y))) -> plusAC(x6,s(plusAC(x,y)))
       plusAC(x6,plusAC(x,s(y))) -> plusAC(x,y)
       plusAC(x5,plusAC(x,0())) -> plusAC(x5,x)
       plusAC(x,s(y)) -> plusAC(x,y)
      Equations:
       plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
       plusAC(x2,x3) -> plusAC(x3,x2)
       timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
       timesAC(x2,x3) -> timesAC(x3,x2)
       plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
       plusAC(x3,x2) -> plusAC(x2,x3)
       timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
       timesAC(x3,x2) -> timesAC(x2,x3)
      TRS:
       plusAC(x,s(y)) -> s(plusAC(x,y))
       plusAC(x,0()) -> x
      S:
       plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
       plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
       timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
       timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(timesAC) = []
        pi(0) = []
        pi(s) = []
       precedence:
        timesAC > plusAC > 0 > s
       status:
        
       problem:
        Equations#:
         plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
         plusAC(x2,x3) -> plusAC(x3,x2)
         timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
         timesAC(x2,x3) -> timesAC(x3,x2)
         plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
         plusAC(x3,x2) -> plusAC(x2,x3)
         timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
         timesAC(x3,x2) -> timesAC(x2,x3)
        DPs:
         
        Equations:
         plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
         plusAC(x2,x3) -> plusAC(x3,x2)
         timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
         timesAC(x2,x3) -> timesAC(x3,x2)
         plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
         plusAC(x3,x2) -> plusAC(x2,x3)
         timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
         timesAC(x3,x2) -> timesAC(x2,x3)
        TRS:
         plusAC(x,s(y)) -> s(plusAC(x,y))
         plusAC(x,0()) -> x
        S:
         plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
         plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
         timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
         timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
       Qed
    
    Equations#:
     plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
     plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
     times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
     times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
     plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
     plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
     times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
     times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
    DPs:
     div#(s(x),s(y)) -> div#(minus(x,y),s(y))
    Equations:
     plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
     plusAC(x2,x3) -> plusAC(x3,x2)
     timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
     timesAC(x2,x3) -> timesAC(x3,x2)
     plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
     plusAC(x3,x2) -> plusAC(x2,x3)
     timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
     timesAC(x3,x2) -> timesAC(x2,x3)
    TRS:
     plusAC(x,0()) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     timesAC(x,0()) -> 0()
     timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     div(0(),s(y)) -> 0()
     div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
    S:
     plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
     plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
     times{AC,#}(timesAC(x9,x10),x11) -> times{AC,#}(x9,x10)
     times{AC,#}(x9,timesAC(x10,x11)) -> times{AC,#}(x10,x11)
    AC-DP unlabeling:
     Equations#:
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
     DPs:
      div#(s(x),s(y)) -> div#(minus(x,y),s(y))
     Equations:
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
     TRS:
      plusAC(x,0()) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      timesAC(x,0()) -> 0()
      timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
      minus(x,0()) -> x
      minus(s(x),s(y)) -> minus(x,y)
      div(0(),s(y)) -> 0()
      div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
     S:
      plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
      plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
      timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
      timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
     Usable Rule Processor:
      Equations#:
       plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
       plusAC(x2,x3) -> plusAC(x3,x2)
       timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
       timesAC(x2,x3) -> timesAC(x3,x2)
       plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
       plusAC(x3,x2) -> plusAC(x2,x3)
       timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
       timesAC(x3,x2) -> timesAC(x2,x3)
      DPs:
       div#(s(x),s(y)) -> div#(minus(x,y),s(y))
      Equations:
       plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
       plusAC(x2,x3) -> plusAC(x3,x2)
       timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
       timesAC(x2,x3) -> timesAC(x3,x2)
       plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
       plusAC(x3,x2) -> plusAC(x2,x3)
       timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
       timesAC(x3,x2) -> timesAC(x2,x3)
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
      S:
       plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
       plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
       timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
       timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(timesAC) = [0,1]
        pi(0) = []
        pi(s) = [0]
        pi(minus) = [0]
        pi(div#) = [0]
       precedence:
        div# > s > minus > timesAC > 0 > plusAC
       status:
        div#:lex  minus:lex  
       problem:
        Equations#:
         plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
         plusAC(x2,x3) -> plusAC(x3,x2)
         timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
         timesAC(x2,x3) -> timesAC(x3,x2)
         plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
         plusAC(x3,x2) -> plusAC(x2,x3)
         timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
         timesAC(x3,x2) -> timesAC(x2,x3)
        DPs:
         
        Equations:
         plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
         plusAC(x2,x3) -> plusAC(x3,x2)
         timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
         timesAC(x2,x3) -> timesAC(x3,x2)
         plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
         plusAC(x3,x2) -> plusAC(x2,x3)
         timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
         timesAC(x3,x2) -> timesAC(x2,x3)
        TRS:
         minus(x,0()) -> x
         minus(s(x),s(y)) -> minus(x,y)
        S:
         plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
         plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
         timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
         timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
       Qed
   
   Equations#:
    plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
    plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
    times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
    times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
    plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
    plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
    times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
    times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
   Equations:
    plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
    plusAC(x2,x3) -> plusAC(x3,x2)
    timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
    timesAC(x2,x3) -> timesAC(x3,x2)
    plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
    plusAC(x3,x2) -> plusAC(x2,x3)
    timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
    timesAC(x3,x2) -> timesAC(x2,x3)
   TRS:
    plusAC(x,0()) -> x
    plusAC(x,s(y)) -> s(plusAC(x,y))
    timesAC(x,0()) -> 0()
    timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    div(0(),s(y)) -> 0()
    div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
   S:
    plus{AC,#}(plusAC(x9,x10),x11) -> plus{AC,#}(x9,x10)
    plus{AC,#}(x9,plusAC(x10,x11)) -> plus{AC,#}(x10,x11)
    times{AC,#}(timesAC(x9,x10),x11) -> times{AC,#}(x9,x10)
    times{AC,#}(x9,timesAC(x10,x11)) -> times{AC,#}(x10,x11)
   AC-DP unlabeling:
    Equations#:
     plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
     plusAC(x2,x3) -> plusAC(x3,x2)
     timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
     timesAC(x2,x3) -> timesAC(x3,x2)
     plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
     plusAC(x3,x2) -> plusAC(x2,x3)
     timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
     timesAC(x3,x2) -> timesAC(x2,x3)
    DPs:
     minus#(s(x),s(y)) -> minus#(x,y)
    Equations:
     plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
     plusAC(x2,x3) -> plusAC(x3,x2)
     timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
     timesAC(x2,x3) -> timesAC(x3,x2)
     plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
     plusAC(x3,x2) -> plusAC(x2,x3)
     timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
     timesAC(x3,x2) -> timesAC(x2,x3)
    TRS:
     plusAC(x,0()) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     timesAC(x,0()) -> 0()
     timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     div(0(),s(y)) -> 0()
     div(s(x),s(y)) -> s(div(minus(x,y),s(y)))
    S:
     plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
     plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
     timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
     timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
    Usable Rule Processor:
     Equations#:
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
     DPs:
      minus#(s(x),s(y)) -> minus#(x,y)
     Equations:
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
     TRS:
      
     S:
      plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
      plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
      timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
      timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
     AC-RPO Processor:
      argument filtering:
       pi(plusAC) = []
       pi(timesAC) = []
       pi(s) = [0]
       pi(minus#) = 1
      precedence:
       minus# > s > timesAC > plusAC
      status:
       minus#:mul  
      problem:
       Equations#:
        plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
        plusAC(x2,x3) -> plusAC(x3,x2)
        timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
        timesAC(x2,x3) -> timesAC(x3,x2)
        plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
        plusAC(x3,x2) -> plusAC(x2,x3)
        timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
        timesAC(x3,x2) -> timesAC(x2,x3)
       DPs:
        
       Equations:
        plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
        plusAC(x2,x3) -> plusAC(x3,x2)
        timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
        timesAC(x2,x3) -> timesAC(x3,x2)
        plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
        plusAC(x3,x2) -> plusAC(x2,x3)
        timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
        timesAC(x3,x2) -> timesAC(x2,x3)
       TRS:
        
       S:
        plusAC(plusAC(x9,x10),x11) -> plusAC(x9,x10)
        plusAC(x9,plusAC(x10,x11)) -> plusAC(x10,x11)
        timesAC(timesAC(x9,x10),x11) -> timesAC(x9,x10)
        timesAC(x9,timesAC(x10,x11)) -> timesAC(x10,x11)
      Qed