YES
Time: 0.353

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,i(x)) -> 0()
  i(0()) -> 0()
  i(i(x)) -> x
  i(plusAC(x,y)) -> plusAC(i(x),i(y))
  timesAC(x,1()) -> x
  timesAC(x,0()) -> 0()
  timesAC(x,i(y)) -> i(timesAC(x,y))
  timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(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:
   i#(plusAC(x,y)) -> i#(y)
   i#(plusAC(x,y)) -> i#(x)
   i#(plusAC(x,y)) -> plus{AC,#}(i(x),i(y))
   times{AC,#}(x,i(y)) -> times{AC,#}(x,y)
   times{AC,#}(x,i(y)) -> i#(timesAC(x,y))
   times{AC,#}(x,plusAC(y,z)) -> times{AC,#}(x,z)
   times{AC,#}(x,plusAC(y,z)) -> times{AC,#}(x,y)
   times{AC,#}(x,plusAC(y,z)) -> plus{AC,#}(timesAC(x,y),timesAC(x,z))
   plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
   plus{AC,#}(x7,plusAC(x,i(x))) -> plus{AC,#}(x7,0())
   times{AC,#}(x8,timesAC(x,1())) -> times{AC,#}(x8,x)
   times{AC,#}(x9,timesAC(x,0())) -> times{AC,#}(x9,0())
   times{AC,#}(x10,timesAC(x,i(y))) -> times{AC,#}(x,y)
   times{AC,#}(x10,timesAC(x,i(y))) -> i#(timesAC(x,y))
   times{AC,#}(x10,timesAC(x,i(y))) -> times{AC,#}(x10,i(timesAC(x,y)))
   times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> times{AC,#}(x,z)
   times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> times{AC,#}(x,y)
   times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> plus{AC,#}(timesAC(x,y),timesAC(x,z))
   times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> times{AC,#}(x11,plusAC(timesAC(x,y),timesAC(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,i(x)) -> 0()
   i(0()) -> 0()
   i(i(x)) -> x
   i(plusAC(x,y)) -> plusAC(i(x),i(y))
   timesAC(x,1()) -> x
   timesAC(x,0()) -> 0()
   timesAC(x,i(y)) -> i(timesAC(x,y))
   timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(x,z))
  S:
   plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
   plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
   times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
   times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
  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:
    i#(plusAC(x,y)) -> i#(y)
    i#(plusAC(x,y)) -> i#(x)
    i#(plusAC(x,y)) -> plus{AC,#}(i(x),i(y))
    times{AC,#}(x,i(y)) -> times{AC,#}(x,y)
    times{AC,#}(x,i(y)) -> i#(timesAC(x,y))
    times{AC,#}(x,plusAC(y,z)) -> times{AC,#}(x,z)
    times{AC,#}(x,plusAC(y,z)) -> times{AC,#}(x,y)
    times{AC,#}(x,plusAC(y,z)) -> plus{AC,#}(timesAC(x,y),timesAC(x,z))
    plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
    plus{AC,#}(x7,plusAC(x,i(x))) -> plus{AC,#}(x7,0())
    times{AC,#}(x8,timesAC(x,1())) -> times{AC,#}(x8,x)
    times{AC,#}(x9,timesAC(x,0())) -> times{AC,#}(x9,0())
    times{AC,#}(x10,timesAC(x,i(y))) -> times{AC,#}(x,y)
    times{AC,#}(x10,timesAC(x,i(y))) -> i#(timesAC(x,y))
    times{AC,#}(x10,timesAC(x,i(y))) -> times{AC,#}(x10,i(timesAC(x,y)))
    times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> times{AC,#}(x,z)
    times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> times{AC,#}(x,y)
    times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> plus{AC,#}(timesAC(x,y),timesAC(x,z))
    times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> times{AC,#}(x11,plusAC(timesAC(x,y),timesAC(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,i(x)) -> 0()
    i(0()) -> 0()
    i(i(x)) -> x
    i(plusAC(x,y)) -> plusAC(i(x),i(y))
    timesAC(x,1()) -> x
    timesAC(x,0()) -> 0()
    timesAC(x,i(y)) -> i(timesAC(x,y))
    timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(x,z))
   S:
    plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
    plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
    times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
    times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
   SCC Processor:
    #sccs: 3
    #rules: 14
    #arcs: 162/361
    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,#}(x11,timesAC(x,plusAC(y,z))) -> times{AC,#}(x11,plusAC(timesAC(x,y),timesAC(x,z)))
     times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> times{AC,#}(x,y)
     times{AC,#}(x11,timesAC(x,plusAC(y,z))) -> times{AC,#}(x,z)
     times{AC,#}(x10,timesAC(x,i(y))) -> times{AC,#}(x10,i(timesAC(x,y)))
     times{AC,#}(x10,timesAC(x,i(y))) -> times{AC,#}(x,y)
     times{AC,#}(x9,timesAC(x,0())) -> times{AC,#}(x9,0())
     times{AC,#}(x8,timesAC(x,1())) -> times{AC,#}(x8,x)
     times{AC,#}(x,plusAC(y,z)) -> times{AC,#}(x,y)
     times{AC,#}(x,plusAC(y,z)) -> times{AC,#}(x,z)
     times{AC,#}(x,i(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,i(x)) -> 0()
     i(0()) -> 0()
     i(i(x)) -> x
     i(plusAC(x,y)) -> plusAC(i(x),i(y))
     timesAC(x,1()) -> x
     timesAC(x,0()) -> 0()
     timesAC(x,i(y)) -> i(timesAC(x,y))
     timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(x,z))
    S:
     plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
     plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
     times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
     times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
    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(x11,timesAC(x,plusAC(y,z))) -> timesAC(x11,plusAC(timesAC(x,y),timesAC(x,z)))
      timesAC(x11,timesAC(x,plusAC(y,z))) -> timesAC(x,y)
      timesAC(x11,timesAC(x,plusAC(y,z))) -> timesAC(x,z)
      timesAC(x10,timesAC(x,i(y))) -> timesAC(x10,i(timesAC(x,y)))
      timesAC(x10,timesAC(x,i(y))) -> timesAC(x,y)
      timesAC(x9,timesAC(x,0())) -> timesAC(x9,0())
      timesAC(x8,timesAC(x,1())) -> timesAC(x8,x)
      timesAC(x,plusAC(y,z)) -> timesAC(x,y)
      timesAC(x,plusAC(y,z)) -> timesAC(x,z)
      timesAC(x,i(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,i(x)) -> 0()
      i(0()) -> 0()
      i(i(x)) -> x
      i(plusAC(x,y)) -> plusAC(i(x),i(y))
      timesAC(x,1()) -> x
      timesAC(x,0()) -> 0()
      timesAC(x,i(y)) -> i(timesAC(x,y))
      timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(x,z))
     S:
      plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
      plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
      timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
      timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
     AC-RPO Processor:
      argument filtering:
       pi(plusAC) = [0,1]
       pi(timesAC) = [0,1]
       pi(0) = []
       pi(i) = [0]
       pi(1) = []
      precedence:
       timesAC > i > plusAC > 0 > 1
      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,i(x)) -> 0()
        i(0()) -> 0()
        i(i(x)) -> x
        i(plusAC(x,y)) -> plusAC(i(x),i(y))
        timesAC(x,1()) -> x
        timesAC(x,0()) -> 0()
        timesAC(x,i(y)) -> i(timesAC(x,y))
        timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(x,z))
       S:
        plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
        plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
        timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
        timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
      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:
     i#(plusAC(x,y)) -> i#(x)
     i#(plusAC(x,y)) -> i#(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,i(x)) -> 0()
     i(0()) -> 0()
     i(i(x)) -> x
     i(plusAC(x,y)) -> plusAC(i(x),i(y))
     timesAC(x,1()) -> x
     timesAC(x,0()) -> 0()
     timesAC(x,i(y)) -> i(timesAC(x,y))
     timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(x,z))
    S:
     plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
     plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
     times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
     times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
    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:
      i#(plusAC(x,y)) -> i#(x)
      i#(plusAC(x,y)) -> i#(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,i(x)) -> 0()
      i(0()) -> 0()
      i(i(x)) -> x
      i(plusAC(x,y)) -> plusAC(i(x),i(y))
      timesAC(x,1()) -> x
      timesAC(x,0()) -> 0()
      timesAC(x,i(y)) -> i(timesAC(x,y))
      timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(x,z))
     S:
      plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
      plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
      timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
      timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
     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:
       i#(plusAC(x,y)) -> i#(x)
       i#(plusAC(x,y)) -> i#(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:
       
      S:
       plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
       plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
       timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
       timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(timesAC) = []
        pi(i#) = [0]
       precedence:
        plusAC > i# > timesAC
       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:
         
        S:
         plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
         plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
         timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
         timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
       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,#}(x7,plusAC(x,i(x))) -> plus{AC,#}(x7,0())
     plus{AC,#}(x6,plusAC(x,0())) -> plus{AC,#}(x6,x)
    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,i(x)) -> 0()
     i(0()) -> 0()
     i(i(x)) -> x
     i(plusAC(x,y)) -> plusAC(i(x),i(y))
     timesAC(x,1()) -> x
     timesAC(x,0()) -> 0()
     timesAC(x,i(y)) -> i(timesAC(x,y))
     timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(x,z))
    S:
     plus{AC,#}(plusAC(x12,x13),x14) -> plus{AC,#}(x12,x13)
     plus{AC,#}(x12,plusAC(x13,x14)) -> plus{AC,#}(x13,x14)
     times{AC,#}(timesAC(x12,x13),x14) -> times{AC,#}(x12,x13)
     times{AC,#}(x12,timesAC(x13,x14)) -> times{AC,#}(x13,x14)
    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(x7,plusAC(x,i(x))) -> plusAC(x7,0())
      plusAC(x6,plusAC(x,0())) -> plusAC(x6,x)
     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,i(x)) -> 0()
      i(0()) -> 0()
      i(i(x)) -> x
      i(plusAC(x,y)) -> plusAC(i(x),i(y))
      timesAC(x,1()) -> x
      timesAC(x,0()) -> 0()
      timesAC(x,i(y)) -> i(timesAC(x,y))
      timesAC(x,plusAC(y,z)) -> plusAC(timesAC(x,y),timesAC(x,z))
     S:
      plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
      plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
      timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
      timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
     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(x7,plusAC(x,i(x))) -> plusAC(x7,0())
       plusAC(x6,plusAC(x,0())) -> plusAC(x6,x)
      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,i(x)) -> 0()
      S:
       plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
       plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
       timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
       timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
      AC-RPO Processor:
       argument filtering:
        pi(plusAC) = [0,1]
        pi(timesAC) = [0,1]
        pi(0) = []
        pi(i) = []
       precedence:
        i > 0 > plusAC > timesAC
       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,i(x)) -> 0()
        S:
         plusAC(plusAC(x12,x13),x14) -> plusAC(x12,x13)
         plusAC(x12,plusAC(x13,x14)) -> plusAC(x13,x14)
         timesAC(timesAC(x12,x13),x14) -> timesAC(x12,x13)
         timesAC(x12,timesAC(x13,x14)) -> timesAC(x13,x14)
       Qed