YES
Time: 0.249

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

Proof:
 DP Processor:
  Equations#:
   times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
   times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
   plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
   plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
   times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
   times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
   plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
   plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
  DPs:
   times{AC,#}(x,s(y)) -> times{AC,#}(x,y)
   times{AC,#}(x,s(y)) -> plus{AC,#}(timesAC(x,y),x)
   plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
   times{AC,#}(x5,timesAC(x,0())) -> times{AC,#}(x5,0())
   times{AC,#}(x6,timesAC(x,s(y))) -> times{AC,#}(x,y)
   times{AC,#}(x6,timesAC(x,s(y))) -> plus{AC,#}(timesAC(x,y),x)
   times{AC,#}(x6,timesAC(x,s(y))) -> times{AC,#}(x6,plusAC(timesAC(x,y),x))
   plus{AC,#}(x7,plusAC(x,0())) -> plus{AC,#}(x7,x)
   plus{AC,#}(x8,plusAC(0(),x)) -> plus{AC,#}(x8,x)
   plus{AC,#}(x9,plusAC(x,s(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x9,plusAC(x,s(y))) -> plus{AC,#}(x9,s(plusAC(x,y)))
   plus{AC,#}(x10,plusAC(s(x),y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x10,plusAC(s(x),y)) -> plus{AC,#}(x10,s(plusAC(x,y)))
  Equations:
   timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
   timesAC(x2,x3) -> timesAC(x3,x2)
   plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
   plusAC(x2,x3) -> plusAC(x3,x2)
   timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
   timesAC(x3,x2) -> timesAC(x2,x3)
   plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
   plusAC(x3,x2) -> plusAC(x2,x3)
  TRS:
   timesAC(x,0()) -> 0()
   timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
   plusAC(x,0()) -> x
   plusAC(0(),x) -> x
   plusAC(x,s(y)) -> s(plusAC(x,y))
   plusAC(s(x),y) -> s(plusAC(x,y))
  S:
   times{AC,#}(timesAC(x11,x12),x13) -> times{AC,#}(x11,x12)
   times{AC,#}(x11,timesAC(x12,x13)) -> times{AC,#}(x12,x13)
   plus{AC,#}(plusAC(x11,x12),x13) -> plus{AC,#}(x11,x12)
   plus{AC,#}(x11,plusAC(x12,x13)) -> plus{AC,#}(x12,x13)
  AC-EDG Processor:
   Equations#:
    times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
    times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
    plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
    plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
    times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
    times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
    plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
    plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
   DPs:
    times{AC,#}(x,s(y)) -> times{AC,#}(x,y)
    times{AC,#}(x,s(y)) -> plus{AC,#}(timesAC(x,y),x)
    plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
    times{AC,#}(x5,timesAC(x,0())) -> times{AC,#}(x5,0())
    times{AC,#}(x6,timesAC(x,s(y))) -> times{AC,#}(x,y)
    times{AC,#}(x6,timesAC(x,s(y))) -> plus{AC,#}(timesAC(x,y),x)
    times{AC,#}(x6,timesAC(x,s(y))) -> times{AC,#}(x6,plusAC(timesAC(x,y),x))
    plus{AC,#}(x7,plusAC(x,0())) -> plus{AC,#}(x7,x)
    plus{AC,#}(x8,plusAC(0(),x)) -> plus{AC,#}(x8,x)
    plus{AC,#}(x9,plusAC(x,s(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x9,plusAC(x,s(y))) -> plus{AC,#}(x9,s(plusAC(x,y)))
    plus{AC,#}(x10,plusAC(s(x),y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x10,plusAC(s(x),y)) -> plus{AC,#}(x10,s(plusAC(x,y)))
   Equations:
    timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
    timesAC(x2,x3) -> timesAC(x3,x2)
    plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
    plusAC(x2,x3) -> plusAC(x3,x2)
    timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
    timesAC(x3,x2) -> timesAC(x2,x3)
    plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
    plusAC(x3,x2) -> plusAC(x2,x3)
   TRS:
    timesAC(x,0()) -> 0()
    timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
    plusAC(x,0()) -> x
    plusAC(0(),x) -> x
    plusAC(x,s(y)) -> s(plusAC(x,y))
    plusAC(s(x),y) -> s(plusAC(x,y))
   S:
    times{AC,#}(timesAC(x11,x12),x13) -> times{AC,#}(x11,x12)
    times{AC,#}(x11,timesAC(x12,x13)) -> times{AC,#}(x12,x13)
    plus{AC,#}(plusAC(x11,x12),x13) -> plus{AC,#}(x11,x12)
    plus{AC,#}(x11,plusAC(x12,x13)) -> plus{AC,#}(x12,x13)
   SCC Processor:
    #sccs: 2
    #rules: 12
    #arcs: 104/196
    Equations#:
     times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
     times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
     plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
     plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
     times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
     times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
     plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
     plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
    DPs:
     times{AC,#}(x6,timesAC(x,s(y))) -> times{AC,#}(x6,plusAC(timesAC(x,y),x))
     times{AC,#}(x6,timesAC(x,s(y))) -> times{AC,#}(x,y)
     times{AC,#}(x5,timesAC(x,0())) -> times{AC,#}(x5,0())
     times{AC,#}(x,s(y)) -> times{AC,#}(x,y)
    Equations:
     timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
     timesAC(x2,x3) -> timesAC(x3,x2)
     plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
     plusAC(x2,x3) -> plusAC(x3,x2)
     timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
     timesAC(x3,x2) -> timesAC(x2,x3)
     plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
     plusAC(x3,x2) -> plusAC(x2,x3)
    TRS:
     timesAC(x,0()) -> 0()
     timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
     plusAC(x,0()) -> x
     plusAC(0(),x) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     plusAC(s(x),y) -> s(plusAC(x,y))
    S:
     times{AC,#}(timesAC(x11,x12),x13) -> times{AC,#}(x11,x12)
     times{AC,#}(x11,timesAC(x12,x13)) -> times{AC,#}(x12,x13)
     plus{AC,#}(plusAC(x11,x12),x13) -> plus{AC,#}(x11,x12)
     plus{AC,#}(x11,plusAC(x12,x13)) -> plus{AC,#}(x12,x13)
    AC-DP unlabeling:
     Equations#:
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
     DPs:
      timesAC(x6,timesAC(x,s(y))) -> timesAC(x6,plusAC(timesAC(x,y),x))
      timesAC(x6,timesAC(x,s(y))) -> timesAC(x,y)
      timesAC(x5,timesAC(x,0())) -> timesAC(x5,0())
      timesAC(x,s(y)) -> timesAC(x,y)
     Equations:
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
     TRS:
      timesAC(x,0()) -> 0()
      timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
      plusAC(x,0()) -> x
      plusAC(0(),x) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      plusAC(s(x),y) -> s(plusAC(x,y))
     S:
      timesAC(timesAC(x11,x12),x13) -> timesAC(x11,x12)
      timesAC(x11,timesAC(x12,x13)) -> timesAC(x12,x13)
      plusAC(plusAC(x11,x12),x13) -> plusAC(x11,x12)
      plusAC(x11,plusAC(x12,x13)) -> plusAC(x12,x13)
     AC-RPO Processor:
      argument filtering:
       pi(plusAC) = [0,1]
       pi(timesAC) = [0,1]
       pi(0) = []
       pi(s) = []
      precedence:
       timesAC > s > plusAC > 0
      status:
       
      problem:
       Equations#:
        timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
        timesAC(x2,x3) -> timesAC(x3,x2)
        plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
        plusAC(x2,x3) -> plusAC(x3,x2)
        timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
        timesAC(x3,x2) -> timesAC(x2,x3)
        plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
        plusAC(x3,x2) -> plusAC(x2,x3)
       DPs:
        
       Equations:
        timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
        timesAC(x2,x3) -> timesAC(x3,x2)
        plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
        plusAC(x2,x3) -> plusAC(x3,x2)
        timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
        timesAC(x3,x2) -> timesAC(x2,x3)
        plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
        plusAC(x3,x2) -> plusAC(x2,x3)
       TRS:
        timesAC(x,0()) -> 0()
        timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
        plusAC(x,0()) -> x
        plusAC(0(),x) -> x
        plusAC(x,s(y)) -> s(plusAC(x,y))
        plusAC(s(x),y) -> s(plusAC(x,y))
       S:
        timesAC(timesAC(x11,x12),x13) -> timesAC(x11,x12)
        timesAC(x11,timesAC(x12,x13)) -> timesAC(x12,x13)
        plusAC(plusAC(x11,x12),x13) -> plusAC(x11,x12)
        plusAC(x11,plusAC(x12,x13)) -> plusAC(x12,x13)
      Qed
    
    Equations#:
     times{AC,#}(timesAC(x2,x3),x4) -> times{AC,#}(x2,timesAC(x3,x4))
     times{AC,#}(x2,x3) -> times{AC,#}(x3,x2)
     plus{AC,#}(plusAC(x2,x3),x4) -> plus{AC,#}(x2,plusAC(x3,x4))
     plus{AC,#}(x2,x3) -> plus{AC,#}(x3,x2)
     times{AC,#}(x2,timesAC(x3,x4)) -> times{AC,#}(timesAC(x2,x3),x4)
     times{AC,#}(x3,x2) -> times{AC,#}(x2,x3)
     plus{AC,#}(x2,plusAC(x3,x4)) -> plus{AC,#}(plusAC(x2,x3),x4)
     plus{AC,#}(x3,x2) -> plus{AC,#}(x2,x3)
    DPs:
     plus{AC,#}(s(x),y) -> plus{AC,#}(x,y)
     plus{AC,#}(x10,plusAC(s(x),y)) -> plus{AC,#}(x10,s(plusAC(x,y)))
     plus{AC,#}(x10,plusAC(s(x),y)) -> plus{AC,#}(x,y)
     plus{AC,#}(x9,plusAC(x,s(y))) -> plus{AC,#}(x9,s(plusAC(x,y)))
     plus{AC,#}(x9,plusAC(x,s(y))) -> plus{AC,#}(x,y)
     plus{AC,#}(x8,plusAC(0(),x)) -> plus{AC,#}(x8,x)
     plus{AC,#}(x7,plusAC(x,0())) -> plus{AC,#}(x7,x)
     plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
    Equations:
     timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
     timesAC(x2,x3) -> timesAC(x3,x2)
     plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
     plusAC(x2,x3) -> plusAC(x3,x2)
     timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
     timesAC(x3,x2) -> timesAC(x2,x3)
     plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
     plusAC(x3,x2) -> plusAC(x2,x3)
    TRS:
     timesAC(x,0()) -> 0()
     timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
     plusAC(x,0()) -> x
     plusAC(0(),x) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     plusAC(s(x),y) -> s(plusAC(x,y))
    S:
     times{AC,#}(timesAC(x11,x12),x13) -> times{AC,#}(x11,x12)
     times{AC,#}(x11,timesAC(x12,x13)) -> times{AC,#}(x12,x13)
     plus{AC,#}(plusAC(x11,x12),x13) -> plus{AC,#}(x11,x12)
     plus{AC,#}(x11,plusAC(x12,x13)) -> plus{AC,#}(x12,x13)
    AC-DP unlabeling:
     Equations#:
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
     DPs:
      plusAC(s(x),y) -> plusAC(x,y)
      plusAC(x10,plusAC(s(x),y)) -> plusAC(x10,s(plusAC(x,y)))
      plusAC(x10,plusAC(s(x),y)) -> plusAC(x,y)
      plusAC(x9,plusAC(x,s(y))) -> plusAC(x9,s(plusAC(x,y)))
      plusAC(x9,plusAC(x,s(y))) -> plusAC(x,y)
      plusAC(x8,plusAC(0(),x)) -> plusAC(x8,x)
      plusAC(x7,plusAC(x,0())) -> plusAC(x7,x)
      plusAC(x,s(y)) -> plusAC(x,y)
     Equations:
      timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
      timesAC(x2,x3) -> timesAC(x3,x2)
      plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
      plusAC(x2,x3) -> plusAC(x3,x2)
      timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
      timesAC(x3,x2) -> timesAC(x2,x3)
      plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
      plusAC(x3,x2) -> plusAC(x2,x3)
     TRS:
      timesAC(x,0()) -> 0()
      timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
      plusAC(x,0()) -> x
      plusAC(0(),x) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      plusAC(s(x),y) -> s(plusAC(x,y))
     S:
      timesAC(timesAC(x11,x12),x13) -> timesAC(x11,x12)
      timesAC(x11,timesAC(x12,x13)) -> timesAC(x12,x13)
      plusAC(plusAC(x11,x12),x13) -> plusAC(x11,x12)
      plusAC(x11,plusAC(x12,x13)) -> plusAC(x12,x13)
     Usable Rule Processor:
      Equations#:
       timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
       timesAC(x2,x3) -> timesAC(x3,x2)
       plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
       plusAC(x2,x3) -> plusAC(x3,x2)
       timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
       timesAC(x3,x2) -> timesAC(x2,x3)
       plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
       plusAC(x3,x2) -> plusAC(x2,x3)
      DPs:
       plusAC(s(x),y) -> plusAC(x,y)
       plusAC(x10,plusAC(s(x),y)) -> plusAC(x10,s(plusAC(x,y)))
       plusAC(x10,plusAC(s(x),y)) -> plusAC(x,y)
       plusAC(x9,plusAC(x,s(y))) -> plusAC(x9,s(plusAC(x,y)))
       plusAC(x9,plusAC(x,s(y))) -> plusAC(x,y)
       plusAC(x8,plusAC(0(),x)) -> plusAC(x8,x)
       plusAC(x7,plusAC(x,0())) -> plusAC(x7,x)
       plusAC(x,s(y)) -> plusAC(x,y)
      Equations:
       timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
       timesAC(x2,x3) -> timesAC(x3,x2)
       plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
       plusAC(x2,x3) -> plusAC(x3,x2)
       timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
       timesAC(x3,x2) -> timesAC(x2,x3)
       plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
       plusAC(x3,x2) -> plusAC(x2,x3)
      TRS:
       plusAC(x,0()) -> x
       plusAC(0(),x) -> x
       plusAC(x,s(y)) -> s(plusAC(x,y))
       plusAC(s(x),y) -> s(plusAC(x,y))
      S:
       timesAC(timesAC(x11,x12),x13) -> timesAC(x11,x12)
       timesAC(x11,timesAC(x12,x13)) -> timesAC(x12,x13)
       plusAC(plusAC(x11,x12),x13) -> plusAC(x11,x12)
       plusAC(x11,plusAC(x12,x13)) -> plusAC(x12,x13)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(timesAC) = [0,1]
        pi(0) = []
        pi(s) = []
       precedence:
        0 > plusAC > s > timesAC
       status:
        
       problem:
        Equations#:
         timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
         timesAC(x2,x3) -> timesAC(x3,x2)
         plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
         plusAC(x2,x3) -> plusAC(x3,x2)
         timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
         timesAC(x3,x2) -> timesAC(x2,x3)
         plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
         plusAC(x3,x2) -> plusAC(x2,x3)
        DPs:
         
        Equations:
         timesAC(timesAC(x2,x3),x4) -> timesAC(x2,timesAC(x3,x4))
         timesAC(x2,x3) -> timesAC(x3,x2)
         plusAC(plusAC(x2,x3),x4) -> plusAC(x2,plusAC(x3,x4))
         plusAC(x2,x3) -> plusAC(x3,x2)
         timesAC(x2,timesAC(x3,x4)) -> timesAC(timesAC(x2,x3),x4)
         timesAC(x3,x2) -> timesAC(x2,x3)
         plusAC(x2,plusAC(x3,x4)) -> plusAC(plusAC(x2,x3),x4)
         plusAC(x3,x2) -> plusAC(x2,x3)
        TRS:
         plusAC(x,0()) -> x
         plusAC(0(),x) -> x
         plusAC(x,s(y)) -> s(plusAC(x,y))
         plusAC(s(x),y) -> s(plusAC(x,y))
        S:
         timesAC(timesAC(x11,x12),x13) -> timesAC(x11,x12)
         timesAC(x11,timesAC(x12,x13)) -> timesAC(x12,x13)
         plusAC(plusAC(x11,x12),x13) -> plusAC(x11,x12)
         plusAC(x11,plusAC(x12,x13)) -> plusAC(x12,x13)
       Qed