YES
Time: 0.651

Problem:
 Equations:
  plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
  plusAC(x3,x4) -> plusAC(x4,x3)
  timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
  timesAC(x3,x4) -> timesAC(x4,x3)
  plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
  plusAC(x4,x3) -> plusAC(x3,x4)
  timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
  timesAC(x4,x3) -> timesAC(x3,x4)
 TRS:
  plusAC(x,0()) -> x
  plusAC(x,s(y)) -> s(plusAC(x,y))
  plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
  timesAC(x,0()) -> 0()
  timesAC(x,timesAC(0(),z)) -> timesAC(0(),z)
  timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
  timesAC(x,timesAC(s(y),z)) -> timesAC(plusAC(timesAC(x,y),x),z)

Proof:
 DP Processor:
  Equations#:
   plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
   plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
   times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
   times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
   plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
   plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
   times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
   times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
  DPs:
   plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
   plus{AC,#}(x,plusAC(s(y),z)) -> plus{AC,#}(x,y)
   plus{AC,#}(x,plusAC(s(y),z)) -> plus{AC,#}(s(plusAC(x,y)),z)
   times{AC,#}(x,s(y)) -> times{AC,#}(x,y)
   times{AC,#}(x,s(y)) -> plus{AC,#}(timesAC(x,y),x)
   times{AC,#}(x,timesAC(s(y),z)) -> times{AC,#}(x,y)
   times{AC,#}(x,timesAC(s(y),z)) -> plus{AC,#}(timesAC(x,y),x)
   times{AC,#}(x,timesAC(s(y),z)) -> times{AC,#}(plusAC(timesAC(x,y),x),z)
   plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
   plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x,y)
   plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x7,s(plusAC(x,y)))
   plus{AC,#}(x8,plusAC(x,plusAC(s(y),z))) -> plus{AC,#}(x,y)
   plus{AC,#}(x8,plusAC(x,plusAC(s(y),z))) -> plus{AC,#}(s(plusAC(x,y)),z)
   plus{AC,#}(x8,plusAC(x,plusAC(s(y),z))) -> plus{AC,#}(x8,plusAC(s(plusAC(x,y)),z))
   times{AC,#}(x9,timesAC(x,0())) -> times{AC,#}(x9,0())
   times{AC,#}(x10,timesAC(x,timesAC(0(),z))) -> times{AC,#}(x10,timesAC(0(),z))
   times{AC,#}(x11,timesAC(x,s(y))) -> times{AC,#}(x,y)
   times{AC,#}(x11,timesAC(x,s(y))) -> plus{AC,#}(timesAC(x,y),x)
   times{AC,#}(x11,timesAC(x,s(y))) -> times{AC,#}(x11,plusAC(timesAC(x,y),x))
   times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) -> times{AC,#}(x,y)
   times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) -> plus{AC,#}(timesAC(x,y),x)
   times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) -> times{AC,#}(plusAC(timesAC(x,y),x),z)
   times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) ->
   times{AC,#}(x12,timesAC(plusAC(timesAC(x,y),x),z))
  Equations:
   plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
   plusAC(x3,x4) -> plusAC(x4,x3)
   timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
   timesAC(x3,x4) -> timesAC(x4,x3)
   plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
   plusAC(x4,x3) -> plusAC(x3,x4)
   timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
   timesAC(x4,x3) -> timesAC(x3,x4)
  TRS:
   plusAC(x,0()) -> x
   plusAC(x,s(y)) -> s(plusAC(x,y))
   plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
   timesAC(x,0()) -> 0()
   timesAC(x,timesAC(0(),z)) -> timesAC(0(),z)
   timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
   timesAC(x,timesAC(s(y),z)) -> timesAC(plusAC(timesAC(x,y),x),z)
  S:
   plus{AC,#}(plusAC(x13,x14),x15) -> plus{AC,#}(x13,x14)
   plus{AC,#}(x13,plusAC(x14,x15)) -> plus{AC,#}(x14,x15)
   times{AC,#}(timesAC(x13,x14),x15) -> times{AC,#}(x13,x14)
   times{AC,#}(x13,timesAC(x14,x15)) -> times{AC,#}(x14,x15)
  AC-EDG Processor:
   Equations#:
    plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
    plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
    times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
    times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
    plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
    plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
    times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
    times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
   DPs:
    plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
    plus{AC,#}(x,plusAC(s(y),z)) -> plus{AC,#}(x,y)
    plus{AC,#}(x,plusAC(s(y),z)) -> plus{AC,#}(s(plusAC(x,y)),z)
    times{AC,#}(x,s(y)) -> times{AC,#}(x,y)
    times{AC,#}(x,s(y)) -> plus{AC,#}(timesAC(x,y),x)
    times{AC,#}(x,timesAC(s(y),z)) -> times{AC,#}(x,y)
    times{AC,#}(x,timesAC(s(y),z)) -> plus{AC,#}(timesAC(x,y),x)
    times{AC,#}(x,timesAC(s(y),z)) -> times{AC,#}(plusAC(timesAC(x,y),x),z)
    plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
    plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x,y)
    plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x7,s(plusAC(x,y)))
    plus{AC,#}(x8,plusAC(x,plusAC(s(y),z))) -> plus{AC,#}(x,y)
    plus{AC,#}(x8,plusAC(x,plusAC(s(y),z))) -> plus{AC,#}(s(plusAC(x,y)),z)
    plus{AC,#}(x8,plusAC(x,plusAC(s(y),z))) -> plus{AC,#}(x8,plusAC(s(plusAC(x,y)),z))
    times{AC,#}(x9,timesAC(x,0())) -> times{AC,#}(x9,0())
    times{AC,#}(x10,timesAC(x,timesAC(0(),z))) -> times{AC,#}(x10,timesAC(0(),z))
    times{AC,#}(x11,timesAC(x,s(y))) -> times{AC,#}(x,y)
    times{AC,#}(x11,timesAC(x,s(y))) -> plus{AC,#}(timesAC(x,y),x)
    times{AC,#}(x11,timesAC(x,s(y))) -> times{AC,#}(x11,plusAC(timesAC(x,y),x))
    times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) -> times{AC,#}(x,y)
    times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) -> plus{AC,#}(timesAC(x,y),x)
    times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) -> times{AC,#}(plusAC(timesAC(x,y),x),z)
    times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) ->
    times{AC,#}(x12,timesAC(plusAC(timesAC(x,y),x),z))
   Equations:
    plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
    plusAC(x3,x4) -> plusAC(x4,x3)
    timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
    timesAC(x3,x4) -> timesAC(x4,x3)
    plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
    plusAC(x4,x3) -> plusAC(x3,x4)
    timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
    timesAC(x4,x3) -> timesAC(x3,x4)
   TRS:
    plusAC(x,0()) -> x
    plusAC(x,s(y)) -> s(plusAC(x,y))
    plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
    timesAC(x,0()) -> 0()
    timesAC(x,timesAC(0(),z)) -> timesAC(0(),z)
    timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
    timesAC(x,timesAC(s(y),z)) -> timesAC(plusAC(timesAC(x,y),x),z)
   S:
    plus{AC,#}(plusAC(x13,x14),x15) -> plus{AC,#}(x13,x14)
    plus{AC,#}(x13,plusAC(x14,x15)) -> plus{AC,#}(x14,x15)
    times{AC,#}(timesAC(x13,x14),x15) -> times{AC,#}(x13,x14)
    times{AC,#}(x13,timesAC(x14,x15)) -> times{AC,#}(x14,x15)
   SCC Processor:
    #sccs: 2
    #rules: 19
    #arcs: 257/529
    Equations#:
     plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
     plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
     times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
     times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
     plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
     plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
     times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
     times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
    DPs:
     times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) -> times{AC,#}(plusAC(timesAC(x,y),x),z)
     times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) ->
     times{AC,#}(x12,timesAC(plusAC(timesAC(x,y),x),z))
     times{AC,#}(x12,timesAC(x,timesAC(s(y),z))) -> times{AC,#}(x,y)
     times{AC,#}(x11,timesAC(x,s(y))) -> times{AC,#}(x11,plusAC(timesAC(x,y),x))
     times{AC,#}(x11,timesAC(x,s(y))) -> times{AC,#}(x,y)
     times{AC,#}(x10,timesAC(x,timesAC(0(),z))) -> times{AC,#}(x10,timesAC(0(),z))
     times{AC,#}(x9,timesAC(x,0())) -> times{AC,#}(x9,0())
     times{AC,#}(x,timesAC(s(y),z)) -> times{AC,#}(plusAC(timesAC(x,y),x),z)
     times{AC,#}(x,timesAC(s(y),z)) -> times{AC,#}(x,y)
     times{AC,#}(x,s(y)) -> times{AC,#}(x,y)
    Equations:
     plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
     plusAC(x3,x4) -> plusAC(x4,x3)
     timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
     timesAC(x3,x4) -> timesAC(x4,x3)
     plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
     plusAC(x4,x3) -> plusAC(x3,x4)
     timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
     timesAC(x4,x3) -> timesAC(x3,x4)
    TRS:
     plusAC(x,0()) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
     timesAC(x,0()) -> 0()
     timesAC(x,timesAC(0(),z)) -> timesAC(0(),z)
     timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
     timesAC(x,timesAC(s(y),z)) -> timesAC(plusAC(timesAC(x,y),x),z)
    S:
     plus{AC,#}(plusAC(x13,x14),x15) -> plus{AC,#}(x13,x14)
     plus{AC,#}(x13,plusAC(x14,x15)) -> plus{AC,#}(x14,x15)
     times{AC,#}(timesAC(x13,x14),x15) -> times{AC,#}(x13,x14)
     times{AC,#}(x13,timesAC(x14,x15)) -> times{AC,#}(x14,x15)
    AC-DP unlabeling:
     Equations#:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     DPs:
      timesAC(x12,timesAC(x,timesAC(s(y),z))) -> timesAC(plusAC(timesAC(x,y),x),z)
      timesAC(x12,timesAC(x,timesAC(s(y),z))) -> timesAC(x12,timesAC(plusAC(timesAC(x,y),x),z))
      timesAC(x12,timesAC(x,timesAC(s(y),z))) -> timesAC(x,y)
      timesAC(x11,timesAC(x,s(y))) -> timesAC(x11,plusAC(timesAC(x,y),x))
      timesAC(x11,timesAC(x,s(y))) -> timesAC(x,y)
      timesAC(x10,timesAC(x,timesAC(0(),z))) -> timesAC(x10,timesAC(0(),z))
      timesAC(x9,timesAC(x,0())) -> timesAC(x9,0())
      timesAC(x,timesAC(s(y),z)) -> timesAC(plusAC(timesAC(x,y),x),z)
      timesAC(x,timesAC(s(y),z)) -> timesAC(x,y)
      timesAC(x,s(y)) -> timesAC(x,y)
     Equations:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     TRS:
      plusAC(x,0()) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
      timesAC(x,0()) -> 0()
      timesAC(x,timesAC(0(),z)) -> timesAC(0(),z)
      timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
      timesAC(x,timesAC(s(y),z)) -> timesAC(plusAC(timesAC(x,y),x),z)
     S:
      plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
      plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
      timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
      timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
     AC-RPO Processor:
      argument filtering:
       pi(plusAC) = [0,1]
       pi(timesAC) = [0,1]
       pi(0) = []
       pi(s) = [0]
      precedence:
       timesAC > 0 > plusAC > s
      status:
       
      problem:
       Equations#:
        plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
        plusAC(x3,x4) -> plusAC(x4,x3)
        timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
        timesAC(x3,x4) -> timesAC(x4,x3)
        plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
        plusAC(x4,x3) -> plusAC(x3,x4)
        timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
        timesAC(x4,x3) -> timesAC(x3,x4)
       DPs:
        
       Equations:
        plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
        plusAC(x3,x4) -> plusAC(x4,x3)
        timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
        timesAC(x3,x4) -> timesAC(x4,x3)
        plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
        plusAC(x4,x3) -> plusAC(x3,x4)
        timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
        timesAC(x4,x3) -> timesAC(x3,x4)
       TRS:
        plusAC(x,0()) -> x
        plusAC(x,s(y)) -> s(plusAC(x,y))
        plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
        timesAC(x,0()) -> 0()
        timesAC(x,timesAC(0(),z)) -> timesAC(0(),z)
        timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
        timesAC(x,timesAC(s(y),z)) -> timesAC(plusAC(timesAC(x,y),x),z)
       S:
        plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
        plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
        timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
        timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
      Qed
    
    Equations#:
     plus{AC,#}(plusAC(x3,x4),x5) -> plus{AC,#}(x3,plusAC(x4,x5))
     plus{AC,#}(x3,x4) -> plus{AC,#}(x4,x3)
     times{AC,#}(timesAC(x3,x4),x5) -> times{AC,#}(x3,timesAC(x4,x5))
     times{AC,#}(x3,x4) -> times{AC,#}(x4,x3)
     plus{AC,#}(x3,plusAC(x4,x5)) -> plus{AC,#}(plusAC(x3,x4),x5)
     plus{AC,#}(x4,x3) -> plus{AC,#}(x3,x4)
     times{AC,#}(x3,timesAC(x4,x5)) -> times{AC,#}(timesAC(x3,x4),x5)
     times{AC,#}(x4,x3) -> times{AC,#}(x3,x4)
    DPs:
     plus{AC,#}(x8,plusAC(x,plusAC(s(y),z))) -> plus{AC,#}(x8,plusAC(s(plusAC(x,y)),z))
     plus{AC,#}(x8,plusAC(x,plusAC(s(y),z))) -> plus{AC,#}(s(plusAC(x,y)),z)
     plus{AC,#}(x8,plusAC(x,plusAC(s(y),z))) -> plus{AC,#}(x,y)
     plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x7,s(plusAC(x,y)))
     plus{AC,#}(x7,plusAC(x,s(y))) -> plus{AC,#}(x,y)
     plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
     plus{AC,#}(x,plusAC(s(y),z)) -> plus{AC,#}(s(plusAC(x,y)),z)
     plus{AC,#}(x,plusAC(s(y),z)) -> plus{AC,#}(x,y)
     plus{AC,#}(x,s(y)) -> plus{AC,#}(x,y)
    Equations:
     plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
     plusAC(x3,x4) -> plusAC(x4,x3)
     timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
     timesAC(x3,x4) -> timesAC(x4,x3)
     plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
     plusAC(x4,x3) -> plusAC(x3,x4)
     timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
     timesAC(x4,x3) -> timesAC(x3,x4)
    TRS:
     plusAC(x,0()) -> x
     plusAC(x,s(y)) -> s(plusAC(x,y))
     plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
     timesAC(x,0()) -> 0()
     timesAC(x,timesAC(0(),z)) -> timesAC(0(),z)
     timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
     timesAC(x,timesAC(s(y),z)) -> timesAC(plusAC(timesAC(x,y),x),z)
    S:
     plus{AC,#}(plusAC(x13,x14),x15) -> plus{AC,#}(x13,x14)
     plus{AC,#}(x13,plusAC(x14,x15)) -> plus{AC,#}(x14,x15)
     times{AC,#}(timesAC(x13,x14),x15) -> times{AC,#}(x13,x14)
     times{AC,#}(x13,timesAC(x14,x15)) -> times{AC,#}(x14,x15)
    AC-DP unlabeling:
     Equations#:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     DPs:
      plusAC(x8,plusAC(x,plusAC(s(y),z))) -> plusAC(x8,plusAC(s(plusAC(x,y)),z))
      plusAC(x8,plusAC(x,plusAC(s(y),z))) -> plusAC(s(plusAC(x,y)),z)
      plusAC(x8,plusAC(x,plusAC(s(y),z))) -> plusAC(x,y)
      plusAC(x7,plusAC(x,s(y))) -> plusAC(x7,s(plusAC(x,y)))
      plusAC(x7,plusAC(x,s(y))) -> plusAC(x,y)
      plusAC(x6,plusAC(x,0())) -> plusAC(x6,x)
      plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
      plusAC(x,plusAC(s(y),z)) -> plusAC(x,y)
      plusAC(x,s(y)) -> plusAC(x,y)
     Equations:
      plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
      plusAC(x3,x4) -> plusAC(x4,x3)
      timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
      timesAC(x3,x4) -> timesAC(x4,x3)
      plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
      plusAC(x4,x3) -> plusAC(x3,x4)
      timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
      timesAC(x4,x3) -> timesAC(x3,x4)
     TRS:
      plusAC(x,0()) -> x
      plusAC(x,s(y)) -> s(plusAC(x,y))
      plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
      timesAC(x,0()) -> 0()
      timesAC(x,timesAC(0(),z)) -> timesAC(0(),z)
      timesAC(x,s(y)) -> plusAC(timesAC(x,y),x)
      timesAC(x,timesAC(s(y),z)) -> timesAC(plusAC(timesAC(x,y),x),z)
     S:
      plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
      plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
      timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
      timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
     Usable Rule Processor:
      Equations#:
       plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
       plusAC(x3,x4) -> plusAC(x4,x3)
       timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
       timesAC(x3,x4) -> timesAC(x4,x3)
       plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
       plusAC(x4,x3) -> plusAC(x3,x4)
       timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
       timesAC(x4,x3) -> timesAC(x3,x4)
      DPs:
       plusAC(x8,plusAC(x,plusAC(s(y),z))) -> plusAC(x8,plusAC(s(plusAC(x,y)),z))
       plusAC(x8,plusAC(x,plusAC(s(y),z))) -> plusAC(s(plusAC(x,y)),z)
       plusAC(x8,plusAC(x,plusAC(s(y),z))) -> plusAC(x,y)
       plusAC(x7,plusAC(x,s(y))) -> plusAC(x7,s(plusAC(x,y)))
       plusAC(x7,plusAC(x,s(y))) -> plusAC(x,y)
       plusAC(x6,plusAC(x,0())) -> plusAC(x6,x)
       plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
       plusAC(x,plusAC(s(y),z)) -> plusAC(x,y)
       plusAC(x,s(y)) -> plusAC(x,y)
      Equations:
       plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
       plusAC(x3,x4) -> plusAC(x4,x3)
       timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
       timesAC(x3,x4) -> timesAC(x4,x3)
       plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
       plusAC(x4,x3) -> plusAC(x3,x4)
       timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
       timesAC(x4,x3) -> timesAC(x3,x4)
      TRS:
       plusAC(x,0()) -> x
       plusAC(x,s(y)) -> s(plusAC(x,y))
       plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
      S:
       plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
       plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
       timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
       timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(timesAC) = [0,1]
        pi(0) = []
        pi(s) = [0]
       precedence:
        plusAC > s > timesAC > 0
       status:
        
       problem:
        Equations#:
         plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
         plusAC(x3,x4) -> plusAC(x4,x3)
         timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
         timesAC(x3,x4) -> timesAC(x4,x3)
         plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
         plusAC(x4,x3) -> plusAC(x3,x4)
         timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
         timesAC(x4,x3) -> timesAC(x3,x4)
        DPs:
         
        Equations:
         plusAC(plusAC(x3,x4),x5) -> plusAC(x3,plusAC(x4,x5))
         plusAC(x3,x4) -> plusAC(x4,x3)
         timesAC(timesAC(x3,x4),x5) -> timesAC(x3,timesAC(x4,x5))
         timesAC(x3,x4) -> timesAC(x4,x3)
         plusAC(x3,plusAC(x4,x5)) -> plusAC(plusAC(x3,x4),x5)
         plusAC(x4,x3) -> plusAC(x3,x4)
         timesAC(x3,timesAC(x4,x5)) -> timesAC(timesAC(x3,x4),x5)
         timesAC(x4,x3) -> timesAC(x3,x4)
        TRS:
         plusAC(x,0()) -> x
         plusAC(x,s(y)) -> s(plusAC(x,y))
         plusAC(x,plusAC(s(y),z)) -> plusAC(s(plusAC(x,y)),z)
        S:
         plusAC(plusAC(x13,x14),x15) -> plusAC(x13,x14)
         plusAC(x13,plusAC(x14,x15)) -> plusAC(x14,x15)
         timesAC(timesAC(x13,x14),x15) -> timesAC(x13,x14)
         timesAC(x13,timesAC(x14,x15)) -> timesAC(x14,x15)
       Qed